Abstract:
A method to forecast a spike price of a commodity may include obtaining a request to perform a prediction of a spike in a price of a commodity. The method may also include obtaining additional information of the commodity based on the input. The method may also include determining, using a first machine learning algorithm, a probability of the spike based at least in part on the additional information. The method may include outputting the probability of the spike for visual representation on an electronic display in response to a determination that the probability of the spike is above a risk tolerance. The method may further include determining, using a second machine learning algorithm, a price prediction in response to a determination that the probability of the spike is below the risk tolerance, wherein determining the price prediction comprises outputting the price prediction for visual representation on the electronic display.

Description:
FIELD 
       [0001]    The present disclosure relates to probabilistic price and spike forecasting. 
       BACKGROUND 
       [0002]    Price forecasting in commodities, such as electricity, has become increasingly important. Price forecasting may range from long-term to short-term forecasting. Long-term and medium-term price forecasting may be used for investment and maintenance objectives. Short-term, such as real-time, forecasting may be used for operation purposes by market operators of the commodity and generators of the commodity. For example, generators of electricity may use real-time price forecasting to determine when and how much to bid for supplying electricity to a marketplace. Others may also use real-time price forecasting for electricity. For instance, retailers and demand response aggregators may use real-time forecasting when determining how to integrate smaller consumers into demand response strategies. 
         [0003]    The subject matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one example technology area where some embodiments described herein may be practiced. 
       SUMMARY 
       [0004]    According to an aspect of an embodiment, a method to forecast a spike price of a commodity may include obtaining a request to perform a prediction of a spike in a price of a commodity. The method may also include obtaining additional information of the commodity based on the input. The method may also include determining, using a first machine learning algorithm, a probability of the spike based at least in part on the additional information. The method may also include outputting the probability of the spike for visual representation on an electronic display in response to a determination that the probability of the spike is above a risk tolerance. The method may further include determining, using a second machine learning algorithm, a price prediction in response to a determination that the probability of the spike is below the risk tolerance, wherein determining the price prediction comprises outputting the price prediction for visual representation on the electronic display. 
         [0005]    The object and advantages of the embodiments will be realized and achieved at least by the elements, features, and combinations particularly pointed out in the claims. 
         [0006]    It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the present disclosure, as claimed. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]    Example embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
           [0008]      FIG. 1  illustrates an example forecast system to forecast price and/or a price spike of a commodity; 
           [0009]      FIG. 2  illustrates a flow diagram of an example method of forecasting a spike price of a commodity; 
           [0010]      FIG. 3  illustrates a flow diagram of another example method of forecasting a spike price of a commodity; 
           [0011]      FIG. 4  illustrates a flow diagram of a further example method of forecasting a spike price of a commodity; and 
           [0012]      FIG. 5A  illustrates an example visualization output of an actual past price and a one-hour-ahead price prediction; 
           [0013]      FIG. 5B  illustrates an example visualization output of a location-specific forecast of price spike likelihood; 
           [0014]      FIG. 6  is a block diagram illustrating an example computing device that is arranged for probabilistic price and spike forecasting, all arranged in accordance with at least one embodiment described herein. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0015]    Some embodiments described in this application relate to a system and method to forecast a price and/or a price spike of a commodity, such as electricity, oil, gas, water, among other commodities. In some circumstances, a commodity market may exist for buying and selling a commodity. The time between the bidding and clearing process may be relatively short, for example every 5, 10, 15, 30, or 60 minutes or some other interval of time. In these and other embodiments, clearing and bidding processes that occur in approximately 60 minutes or less may be referred to herein as real-time pricing of the commodity. Due to recent changes in technology that allow for the real-time pricing of commodities, buyers and sellers may submit bidding prices in real-time. 
         [0016]    Typically, prices of commodities may be volatile and contain price spikes. Price spikes may include instances where the price of the commodity moves in a comparatively large upward or downward trend in a short period of time. For example, in some circumstances, clearing and bidding process for electricity may occur every five minutes. In these and other embodiments, the price may be $100 per megawatt hour (Mwh) at time A and five minutes later at time B, the price may be $300/Mwh. The change of the price between time A and time B may be referred to as a price spike. Further, some prices of commodities may vary by region. For example, electricity demand may be specific to a particular market, country, system and/or locale. Due to the volatility in the prices of commodities, it may be very difficult to submit selling and bidding prices within a proper risk tolerance in real-time and/or for a particular region. Further, conventional systems typically may not predict spikes and spike prices because the conventional systems typically predict prices based on cyclical patterns and spikes and spike prices often do not follow a cyclical pattern. 
         [0017]    To help buyers and sellers manage risk when submitting prices and bids for a commodity, the system and method described in at least some embodiments in this application forecast a price and/or a price spike of a commodity at a particular future time. The buyers and sellers may also use the system and method described to determine a risk tolerance and spike level threshold. Due to the volatile and price spikes of commodity prices, the system and method described in at least some embodiments in this application apply past price and demand data to forecast a price and/or a price spike of a commodity at a particular future time. 
         [0018]    The system and method described may include price spike and probabilistic price forecasting for a specific location and time. An example algorithm may provide forecasting of price spike likelihood for each five-minute interval during an hour period, where the hour period is three hours ahead of a first interval. Another example algorithm may provide forecasting of price spike likelihood for each hour, three hours ahead of the first hour. A further example algorithm may provide non-spike price forecasting for each five-minute interval during an hour period, where the hour period is three hours ahead of the first interval. Yet another example algorithm may provide probabilistic and point price predictions for each five-minute interval during an hour period, where the hour period is three hours ahead of the first interval. 
         [0019]    The system and method described may use random forest and quantile regression on historical load, price, and time/date/location features, up to a year ahead of the point of prediction, to build a predictive model. The combination of methods allows the use of the strengths of both a flexible ensemble of decision trees to predict seemingly unpredictable price spikes, as well as time-series regression, which may take advantage of the underlying structure of the non-spike pricing data. 
         [0020]    In addition to predicting commodity prices, the described methods and systems may be applied to other areas, such as in prediction in fields with volatile time-series data with costly spikes, demands, loads, store inventories, financial data, holiday schedules, markets in which participants may have fixed or varying operating costs, or sell/buy points, and in prediction in other (emerging) energy markets, among others. Embodiments of the present disclosure will be explained with reference to the accompanying drawings. 
         [0021]      FIG. 1  illustrates an example forecast system  100  to forecast price and/or a price spike of a commodity, arranged in accordance with at least one embodiment of the present disclosure. The forecast system  100  may forecast price and/or a price spike of a commodity at a future time based on price information and load information for the commodity. In general, the forecast system  100  may forecast price and/or a price spike of a commodity using one or more models. For example, a model for predicting price and/or a price spike may include a random forest model or a quantile regression model, among others. For example, the forecast system  100  may include hardware, software, or both hardware and software used to perform the methods illustrated in  FIGS. 2 and 4 . 
         [0022]    To forecast a price and/or a price spike of the commodity, the forecast system  100  may obtain a particular time in the future  102  and a location  103  for which the price and/or a price spike of the commodity is to be forecasted. In some embodiments, the time  102  and location  103  may be provided automatically by another system that is requesting the forecast price and/or a price spike or by a user of the forecast system  100  or communicating with the forecast system  100 . In some embodiments, the forecast system  100  may obtain the time  102  based on the time of the request to forecast a price and/or a price spike. For example, in some embodiments, the forecast system  100  may forecast a price and/or a price spike at a particular time ahead of when a request is received. The location  103  may be any physical geographic location, region or area, such as a state, county, district, an area covered by a particular utility provider, etc. In some embodiments, the forecast system  100  may obtain the location  103  based on a geographical location of a user and/or a user device requesting to forecast the price and/or the price spike of the commodity. The geographic location may be obtained via a GPS or other device. In some alternative embodiments, the forecast system  100  may obtain the location  103  from a user of the forecast system  100 . 
         [0023]    The time  102  may be a single time in the future or may be multiple times in the future. The forecast system  100  is described with respect to  FIG. 1  with respect to a single time in the future. However, the forecast system  100  may operate to forecast prices at multiple times by performing multiple iterations. In some embodiments, some data used or generated in one iteration may be used in additional iterations. 
         [0024]    In some embodiments, the time  102  may have a granularity associated with a time granularity of bidding and selling on a commodity market of the commodity. For example, the commodity market for electricity sells and buys electricity at five (5) minute intervals. In these and other embodiments, the time  102  obtained may correspond to the intervals of the commodity market of the commodity. Alternately or additionally, the forecast system  100  may obtain any time and may process the time such that it corresponds with the time intervals of the commodity market of the commodity, such as for every hour, for five minute intervals within an hour, etc. 
         [0025]    The forecast system  100  may also obtain spike risk tolerance and spike price threshold information  104 . The forecast system  100  may obtain the spike risk tolerance from a user of the forecast system  100 . The spike risk tolerance may include one or more alphanumeric values that may be indicative of a particular risk tolerance of the user. In at least one embodiment, the spike risk tolerance may be a predetermined value. The spike price threshold may be determined based on the stability of the price of the commodity. For example, the spike price threshold may be set at a value such that eighty (80) percent of the prices of the commodity within a given time frame are lower than the spike price threshold. In some embodiments, commodity markets with higher price stability may have a higher percent of prices within a given time frame that are lower than the spike price threshold than commodity markets with lower price stability. Alternately or additionally, the spike price threshold may be variable as the stability of the price may vary over time. For example, electricity stability may be different during spring than during summer. In some embodiments, the spike price threshold may be determined based on a knee point of a frequency of the prices in the commodity market. 
         [0026]    Based on the time  102  and location  103 , the forecast system  100  may obtain data regarding the price and load of the commodity. In some embodiments, price information  106  may be obtained about the commodity. Alternately or additionally, load information  108  may be obtained about the commodity. In some embodiments, the price information  106  and the load information  108  may be obtained from the commodity market that handles the selling and buying of the commodity. 
         [0027]    In some embodiments, the price information  106  may include multiple different types of price information. The different types of the price information  106  may include first and second previous price data. For example, in some embodiments, the first previous price data may be actual price data of a first period that is a first time before the time  102  and the second previous price data may be actual price data of a second period that is a second time before the time  102 . In some embodiments, the first and second previous price data may provide price data for multiple buying and selling periods of the commodity market. In some embodiments, the price information  106  may include a difference between the first and second previous price data. 
         [0028]    In some embodiments, the first period may be a period within a few hours of the time  102  to capture current price data trends of the commodity. In some embodiments, the first period may be a period associated with the latest real-time price data of the commodity. The second period may be a period during the same time of day as the time  102  but during a previous day. The second period may assist the forecast system  100  in determining common price trends for the commodity during common hours of the day. For example, electricity prices during the noon hour a day before may be more representative of electricity prices during the noon hour of the current day than electricity prices between 2 and 3 A.M. the day before. 
         [0029]    As an example of the first and second periods, when the commodity market buys and sells every five (5) minutes, the first period may be one hour that spans from two hours to one hour before the time  102 . The second period may also be one hour that spans from twenty-four hours to twenty-three hours before the time  102 . For example, if the time  102  is 12:05 P.M. on April 14, the first previous price data may be 12 equally spaced data points of actual price data of the commodity from 10:05 A.M. to 11:05 A.M. on April 14. The second previous price data may be 12 equally or unequally spaced data points of actual price data of the commodity from 12:05 P.M. to 1:05 P.M. on April 13. In some embodiments, the first and second periods may be different lengths. 
         [0030]    Another type of price information  106  may include a future market clearing price. A future market clearing price may be a predicted price of the commodity at a lower granularity than the requested forecast price and the timing for bidding and clearing of the commodity. For example, the commodity market may accept bids and clear the commodity every 5 minutes. The future market clearing price may provide an estimated price for every hour on the hour. Thus, the future market clearing price may provide an estimate for one or every twelve buying and clearing periods. 
         [0031]    In some embodiments, the load information  108  may include multiple different types of load information. The different types of the load information  108  may include previous load data and forecasted load data. In some embodiments, the previous load data may be the actual load data of a load period that is before the time  102 . The load period of the previous load data may assist the forecast system  100  in determining current load trends of the commodity. In some embodiments, the load information  108  may include a difference between the previous load data and the forecasted load data. 
         [0032]    As an example of the load period when the commodity market buys and sells every 5 minutes, the load period may be one hour that spans from two hours to one hour before the time  102 . For example, if the time  102  is 12:05 P.M. on April 14, the previous load data may be 12 equally or unequally spaced data points of actual load data of the commodity from 10:05 A.M. to 11:05 A.M. on April 14. 
         [0033]    A forecasted load data may be a predicted load of the commodity at a lower granularity than the requested forecast price and the timing for bidding and clearing of the commodity. For example, the commodity market may accept bids and clear the commodity every 5 minutes and provide load information every 5 minutes. The forecasted load data may provide an estimated load for every hour on the hour. Thus, the forecasted load data may provide an estimate for one or every twelve bidding and clearing periods. 
         [0034]    The forecast system  100  may include a data processor  110  to process the price information  106  and the load information  108 . The data processor  110  may remove bad data and interpolate missing data from the price information  106  and the load information  108 . For example, the load information  108  may include load points that indicate that the load is zero. These load points may be replaced with adjusted load values that are interpolated based on neighboring load points. As another example, the price information  106  may include price points that are below zero or zero. These price points may be replaced with adjusted price values that are interpolated based on neighboring price points. The data processor  110  may generate processed load information  112  and processed price information  114 . 
         [0035]    The forecast system  100  may include a price data decomposer  120  to determine spike price information  122  and non-spike price information  124  from the processed price information  114 . The price data decomposer  120  may identify and remove price spikes from the processed price information  114 . In at least one embodiment, price spikes of the processed price information  114  may be identified based on the spike risk tolerance and/or spike price threshold  104 . 
         [0036]    To determine the non-spike price information  124 , the identified price spikes from the processed price information  114  may be removed. Removing the identified price spikes may include changing the price value of the identified price spikes to an interpolated value based on neighboring non-spike price values. 
         [0037]    To determine the spike price information  122 , the identified price spikes from the processed price information  114  may be reduced with the interpolated value for the identified price spikes that replace the price spikes in the non-spike price information  124 . Non-spikes prices may be removed. As a result, the spike price information  122  may include the identified prices spikes with the adjusted values. 
         [0038]    The price data decomposer  120  may individually determine spike price information  122  and non-spike price information  124  for each of the different types of price information. Thus, the first previous price data may be decomposed based on the first previous price data. The second previous price data may be decomposed based on the second previous price data and the future market clearing price may be decomposed based on the future market clearing price. 
         [0039]    In some embodiments, the price data decomposer  120  may determine the processed price information  114  using a moving-average filter of prices values with a rolling window that compares the spike price threshold. In these and other embodiments, the rolling window size may be based on an average length of spike events. In some embodiments, the rolling window size for a commodity market that includes bidding and clearing price points that occur every five (5) minutes may include three (3) to six (6) price points. In these and other embodiments, a moving-average filter may be applied to the non-spike price information  124  after the price spikes have been removed to smooth the prices in the non-spike price information  124 . 
         [0040]    The forecast system  100  may include a feature generator  130 . After the non-spike price information  124  and the spike price information  122  is determined, the feature generator  130  may perform feature generation using the processed load information  112 , the processed price information  114 , the spike price information  122 , and the non-spike price information  124 . The features generated by the feature generation  130  may include spike detection features  140   a , spike price features  140   b , and non-spike price features  140   c , collectively referred to in the current disclosure as the features  140 . Other features  140  may include a day of a week, season, month, day, year, location, hour, minute, derivatives of a smoothed load, price variables, day-ahead price, a difference between forecast and actual loads, prices, number of spikes in an hour, whether or not there are spikes in lagged hours, minimum and maximum temperature at the location, largest absolute deviation in temperature at the location, real-time loads, load forecasts, lagged values of price, load, and spike variables (values three hours ago, at the same time one day prior, at the same time one week prior, and during the same month and season last year), quantile values during the same month last year, spike statistics and frequency during the same month last year, among other features. 
         [0041]    The spike detection features  140   a  may be generated using the processed price information  114  and the processed load information  112 . The spike price features  140   b  may be generated using the processed load information  112  and the spike price information  122  without using the non-spike price information  124  or the processed price information  114 . The non-spike price feature  140   c  may be generated using the processed load information  112  and the non-spike price information  124  without using the spike price information  122  or the processed price information  114 . 
         [0042]    In some embodiments, the spike detection features  140   a , the spike price features  140   b , and the non-spike price features  140   c  may include similar features or non-similar features. Various features that may be included in the spike detection features  140   a , the spike price features  140   b , and the non-spike price features  140   c  are now described. The discussion that follows regarding the various features refers generally to price data. The price data may represent the processed price information  114 , the spike price information  122 , and the non-spike price information  124 . For example, if the discussed features are the non-spike price features  140   c , then the price data may represent the non-spike price information  124 . 
         [0043]    The features  140  generated by the feature generator  130  may include a spike feature, a load feature, a comparison load feature, a seasonal feature, a type of day feature, a hourly price variance feature, a price data feature, a demand price ratio feature, an elastic feature, and a spike series length feature, among other features. 
         [0044]    The spike feature may indicate if a spike occurred in the first previous price data. The load feature may include a normalization of the previous load data of the load information  108 . A generic normalization equation may be applied when generating the features  140 . The generic normalization equation may normalize the data by taking a difference between a value of a data point at a time t and a lowest value in the data set and dividing the difference by a difference between a maximum value and the lowest value in the data set. The result is used to replace the value of the data point at time t such that the data point at time t is normalized. 
         [0045]    The comparison load feature may be a difference between normalized forecasted load data and normalized previous load data. The seasonal feature may be a number that indicates a season, such as spring (March to May), summer (June to August), fall (September to November), and winter (December to February), of the day for the forecasted price being generated. The seasonal feature may be used when training data that is used to generate algorithms, such as a spike detection algorithm  154   a , spike price algorithms  154   b , and a non-spike price algorithm  154   c  that may use the features as inputs and include data from multiple different seasons. If the training data included information from a single season or the commodity&#39;s price does not vary based on a season, then the seasonal feature may not be used. 
         [0046]    The type of day feature may be a number that indicates if the day for the forecasted price being generated is a weekday or a weekend. The day feature may be used when training data used to generate algorithms, such as a spike detection algorithm  154   a , spike price algorithms  154   b , and a non-spike price algorithm  154   c  that may use the features as inputs, include data from every day of the week. If the training data includes information from weekend or weekdays but not both or the commodity&#39;s price does not vary based on a whether it is a weekend or weekday, then the day feature may not be used. 
         [0047]    The hourly price variance feature may be a number that represents a variation of the first previous price data. The price data feature may include a normalization of the one or more of a first and second previous price data and the future market clearing price. 
         [0048]    The demand price ratio feature may include a comparison between the previous load data and the first previous price data after the previous load data and the first previous price data are normalized. The elastic feature may include a comparison between a change over time of the previous load data and a change over time of the first previous price data after the previous load data and the first previous price data are normalized. The spike series length feature may describe the number of consecutive price points that are price spikes. In some embodiments, the spike series length feature may be a number that is one less than the number of consecutive price points that are price spikes from the first previous price data. 
         [0049]    In some embodiments, each of the spike detection features  140   a , the spike price features  140   b , and the non-spike price features  140   c  may include all of the features described in this disclosure among other features generated using the particular price data for that feature group. Alternately or additionally, each of the spike detection features  140   a , the spike price features  140   b , and the non-spike price features  140   c  may include one or more of the features described in this disclosure among other features generated using the particular price data for that feature group. 
         [0050]    For example, in some embodiments, the spike detection features  140   a  may include the spike feature, the load feature, the comparison load feature, the seasonal feature, the type of day feature, the hourly price variance feature, the price data feature, and the spike series length feature. These features may be generated using the processed price information  114  that includes the price spikes. 
         [0051]    In these and other embodiments, the spike price features  140   b  may include the spike feature, the comparison load feature, the price data feature, the demand price ratio feature, and the spike series length feature. These features may be generated using the spike price information  122  and not using the non-spike price information  124  or the processed price information  114 . 
         [0052]    In these and other embodiments, the non-spike price features  140   c  may include the load feature, the comparison load feature, the seasonal feature, the type of day feature, the hourly price variance feature, the price data feature, the demand price ratio feature, and the elastic feature. These features may be generated using the non-spike price information  124  and not using the spike price information  122  or the processed price information  114 . The spike detection features  140   a , spike price features  140   b , and the non-spike price features  140   c  may be provided to the model manager  150 . 
         [0053]    The model manager  150  may create, train, and execute one or more models  152  for price and spike forecasting. Example models  152  may include a time-based (e.g., 5 minute, one hour) spike prediction random forest model and a time-series quantile regression model. A model  152  may include one or more algorithms  154 . For example, the model manager  150  may create and train one or more algorithms  154  that may be used in a price model and/or spike model. Example algorithms  154  may include a spike detection algorithm, spike price algorithm, and a non-spike price algorithm. 
         [0054]    The model manager  150  may generate and/or train models  152  such as by using machine learning algorithms using the price information  106  and the load information  108 . In some embodiments, the models  152  may each result from the same type of machine learning algorithms and may each be trained with similar or different data. In some embodiments, the models  152  may each result from different types of machine learning algorithms. For example, a random forest model may result from a binary classification machine learning algorithm, or using an aggregated “spike hour” variable as a predicted value. The quantile regression model may result from a binary classification machine learning algorithm or by using a real-time price as a predicted value. The models may be trained using some or all of the data available to the model manager  150 . Data used to train a model may be referred to as “training data.” Training data may include previous price and load information about the commodity. For example, the training data may include previous real-time price information, previous future market clearing prices, previous real-time load prices, and previous forecasted load prices, etc. 
         [0055]    In these and other embodiments, the training data used to develop each of the models  152  may be different. For example, the training data may include multiple features based on load information and previous spike-price information of the commodity. To develop each of the models  152 , a different subset of the multiple features and/or different initial training parameters may be provided to the clustering algorithm to develop each one of the models  152 . Thus, each of the models  152  may be similar but different enough to generate a probabilistic array of outputs with the same inputs. In some embodiments, the training data may be updated or added to at particular intervals, such as daily, weekly, bi-weekly, monthly, etc. After a change in the training data, the models  152  may be retrained with the updated training data. 
         [0056]    During execution of one or more models, any of the features  140  may be provided to the model manager  150  as input. The model manager  150  may provide any of the features  140  to an algorithm  154  in the model  152 . For example, the model manager  150  may provide spike detection features to a spike detection algorithm, spike price features to spike price algorithms, and non-spike price features to non-spike price algorithms. A spike detection algorithm may generate spike information  160   a . The spike information  160   a  may indicate if a price spike is forecasted to occur or not to occur at the time  102 . In some embodiments, the spike information  160   a  may be binary and thus may forecast a price spike or no price spike. Alternately or additionally, the spike information  160   a  may provide a probability for an occurrence of the price spike at the time  102 . The model manager  150  may use provided spike price features  140   b  to a spike price algorithm to generate the spike prices  160   b . The model manager  150  may use non-spike price features  140   c  in a non-spike price algorithm  154   c  to generate a non-spike price  160   c.    
         [0057]    The forecast system  100  may include a spike selector  170  to determine a forecasted spike  174  based on the spike information  160   a . The forecast system  100  may include a price selector  172  to determine a forecasted price  176  of the commodity at the time  102  based on the spike prices and non-spike prices  160 . When the spike selector  170  does not forecast a price spike at the time  102 , the price selector  172  may select the non-spike price  160   c  as the forecasted price  176  of the commodity at the time  102 . When the spike selector  170  forecasts a price spike at the time  102 , the forecasted price  176  of the commodity at the time  102  may be based on the spike prices  160   b . In some embodiments, the price selector  172  may determine the forecasted price  176  of the commodity at the time  102  based on the spike prices  160   b  by determining a mean or median of two or more of the spike prices  160   b.    
         [0058]    The forecast system  100  may store various data in a data storage  180 . The data storage  180  may be used to store the time  102 , location  103 , spike risk tolerance and price threshold  104 , processed load information  112 , processed price information  114 , spike price information  122 , non-spike price information  124 , features  140 , algorithms  154 , spike information  160   a , spike prices  160   b , non-spike prices  160   c , forecasted spike  174  and forecasted price  176 . In at least one embodiment, the data storage  180  may include a memory (e.g., random access memory), a cache, a drive (e.g., a hard drive), a flash drive, a database system, or another type of component or device capable of storing data. The data storage  180  may also include multiple storage components (e.g., multiple drives or multiple databases) that may span multiple computing devices (e.g., multiple server computers). The data storage  180  may be implemented within the forecast system  100 . Alternatively, the data storage  180  may be external to the forecast system  100  and communicatively coupled to the forecast system  100  via a data link, such as a wired or wireless connection. The data storage  180  may be configured to store price information  106  and load information  108 . In some embodiments, the price information  106  and load information  108  may be provided to the data storage  180  by a commodity market of the commodity. Upon request from another system, the data storage  180  may be configured to provide the price information  106  and load information  108  over a network (not illustrated). 
         [0059]      FIGS. 2-4  illustrate flow diagrams of example methods related to forecasting price and/or a spike price of a commodity. The methods may be performed by processing logic that may include hardware (circuitry, dedicated logic, etc.), software (such as is run on a general purpose computer system or a dedicated machine), or a combination of both, which processing logic may be included in the forecasting system  100  of  FIG. 1 , or another computer system or device. However, another system, or combination of systems, may be used to perform the methods. For simplicity of explanation, methods described herein are depicted and described as a series of acts. However, acts in accordance with this disclosure may occur in various orders and/or concurrently, and with other acts not presented and described herein. Further, not all illustrated acts may be used to implement the methods in accordance with the disclosed subject matter. In addition, those skilled in the art will understand and appreciate that the methods may alternatively be represented as a series of interrelated states via a state diagram or events. Additionally, the methods disclosed in this specification are capable of being stored on an article of manufacture, such as a non-transitory computer-readable medium, to facilitate transporting and transferring such methods to computing devices. The term article of manufacture, as used herein, is intended to encompass a computer program accessible from any computer-readable device or storage media. Although illustrated as discrete blocks, various blocks may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation. 
         [0060]      FIG. 2  illustrates a flow diagram of an example method  200  of forecasting a spike price of a commodity. The method  200  may begin at block  205 , where processing logic may obtain input pertaining to a prediction of a spike price for a commodity. The input may include a particular time in the future, a location, a spike risk tolerance, and/or a spike price threshold. The input may be provided from a user, a system, randomly generated, a combination thereof, or otherwise obtained. 
         [0061]    At block  210 , the processing logic may obtain additional information based on the input that may be used to determine the prediction of the spike price for the commodity. The additional information may include historical and day-ahead data, real-time loads, prices, and/or weather data, among others. The processing logic may use some of all of the input obtained at block  205  to obtain the additional information. For example, the processing logic may use time and location to obtain historical data and load data for a particular region. 
         [0062]    At block  215 , the processing logic may perform data processing on the input and/or the additional information. For example, the processing logic may preprocess and standardize some or all of the input and/or the additional information. For example, the processing logic may remove duplicate data, and may reformat and/or clean the input and/or the additional information for use in price spike prediction. 
         [0063]    At block  220 , the processing logic may perform feature extraction. In at least one embodiment, the processing logic may extract one or more features from the input and/or additional information. A feature may include any of the features  140  as further described in conjunction with  FIG. 1 . The processing logic may extract features using permutations of a raw dataset (e.g., the input and/or additional information). The processing logic, for example, may extract features for a particular time and/or location. For example, the time may be one hour and the processing logic may observe for price spikes during that one hour. The processing logic may use a spike price threshold to determine whether an observation represents a spike. The processing logic may aggregate the number of spikes that occurred during that observation&#39;s hour. In at least one embodiment, the processing logic may obtain lagged values of variables to receive historical information. In at least one embodiment, the processing logic may calculate a difference between forecast and actual loads and prices. In at least one embodiment, the processing logic may derive variables, such as a day of the week, time, month, location, etc., from observation timestamps. The processing logic may store any of the extracted and calculated features in a data storage. 
         [0064]    At blocks  225 ,  230  and  235 , the processing logic may train or retrain one or more models for predicting spike and price. The processing logic may perform any of blocks  225 ,  230  or  235 . The processing logic may train a random forest model, for example. 
         [0065]    A random forest model may include a bootstrap aggregated ensemble of decision trees. The processing logic may feed each decision tree with different data or different subsets of data from an overall data set. Each tree in the random forest model may yield a recommendation for a particular predicted value based on a terminal node of each observed decision tree. The recommendations from each decision tree may be considered and may be used to generate an output, which may be a spike. By using a random forest model, bias in prediction estimates may be reduced by increasing a number of leafs, levels, or splits for each decision tree. The processing logic may tune (e.g., train) the decision trees to reduce errors in model prediction. 
         [0066]    Random forest modeling may reduce the error due to variance in the data by using input from a greater number of trees to make the model prediction. In addition, with bootstrap aggregated (e.g., “bagging”), the processing logic may train each tree on a subset of the data, instead of the entire dataset. Further, when making a prediction, each tree may consider a subset of the features when choosing which variable to make a split upon at that level. This ensures that the trees are varied individually as well as in the aggregate. 
         [0067]    Random forest modeling may include a more flexible method than some regression-based methods because random forest modeling may rely upon discriminating splits, instead of relying on a simplifying mathematical structure (such as linearity in the data), to make predictions. Random forest modeling may thus be more useful to identify a probability of future spikes because a random forest model may identify patterns in the aggregate dataset without relying on clear mathematical trends in prices (which spikes may not follow). 
         [0068]    To build the random forest model, the processing logic may select a split for each level of each individual decision tree based on which feature and corresponding value most increases a dissimilarity between two groups of data that are created by splitting on that feature and corresponding value. 
         [0069]    An example random forest algorithm, as described in T. Hastie, R. Tibshirani, J. Friedman.  The Elements of Statistical Learning  (2 nd  ed.). New York: Springer Series in Statistics, 2009. Web. October 2015, and incorporated in this disclosure in its entirety, may be as follows: 
         [0070]    1. For b=1 to B:
       (a) Draw a bootstrap sample Z* of size N from the training data.   (b) Grow a random-forest tree T b  to the boostrapped data, by recursively repeating the following steps for each terminal node of the tree, until the minimum node size n min  is reached.
           (i) Select m variables at random from the p variables.   (ii) Pick the best variable/split-point among the m.   (iii) Split the node into two daughter nodes.   
               
 
         [0076]    2. Output the ensemble of trees {Tb} 1   B . 
         [0077]    To make a prediction at a new point x: 
         [0000]    
       
         
           
             
               Regression 
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             Classification: Let Ĉ b  (x) be the class prediction of the bth random-forest tree. Then Ĉ rf   B =majority vote {Ĉ b (x)} 1   B . 
           
         
       
     
         [0079]    Parameters that the processing logic may use to tune the model and optimize performance include a number of features considered at each level to define a split, a minimum number of observations in each terminal node of a tree, a number of trees total in the ensemble, among others. 
         [0080]    At block  225 , the processing logic may train a five-minute spike prediction model which may be used to provide forecasting of price spike likelihood for each five-minute interval within an hour. In at least one embodiment, the five-minute non-spike price prediction model may be used to predict a price spike approximately three hours ahead of the first five-minute interval. In at least one embodiment, the processing logic may train a five-minute non-spike prediction model which may be used to provide forecasting of non-spike price for each five-minute interval within an hour. In at least one embodiment, the five-minute non-spike price prediction model may be used to predict a non-spike price approximately three hours ahead of the first five-minute interval. 
         [0081]    At block  230 , the processing logic may train an hourly spike prediction model which may be used to provide forecasting of price spike likelihood on an hourly level of granularity. In at least one embodiment, the hourly spike prediction model may be used to predict an hourly price spike approximately three hours ahead of the first hour. 
         [0082]    At block  235 , the processing logic may train a quantile regression model on the dataset of features. In at least one embodiment, the processing logic may train a quantile regression model with a real-time price as a predicted value. In at least one embodiment, the processing logic may train the model on a complete dataset, or a dataset of non-spike prices. 
         [0083]    A quantile regression model may provide a model to predict a target variable while assuming that the target variable falls within each of the quantile ranges. As described in R. Koenker, K. Hallock. “Quantile Regression.”  Journal of Economic Perspectives , Vol. 15, No. 4 (2001): 143-156, which is incorporated in this disclosure in its entirety, a quantile function may be found by solving the following optimization problem: 
         [0000]      {circumflex over (β)}(τ)=argmin βε             p Σρ τ (γ i   −x ′β),
 
         [0084]    where ρ τ (u)=u(τ−I(u&lt;0)), the piecewise linear “check function.” 
         [0085]    A parameter that may be used to tune a quantile regression model and optimize performance may include a quantile chosen to define models over, which may determine ρ τ (u). Another parameter that may be used to tune a quantile regression model and optimize performance may include an optimization strategy chosen to solve the optimization function and fit the quantile regression models. 
         [0086]    In at least one embodiment, the processing logic may identify how likely each quantile prediction is for a given observation given the quantile regression models and each of their resulting predicted values output. A prediction from the random forest model may be used for this purpose, as further described in conjunction with  FIGS. 3 and 4 . 
         [0087]    At block  240 , the processing logic may obtain point-of-prediction feature values. The point-of-prediction feature values may be features that may pertain to a prediction to be made. For example, the processing logic may receive a request to predict spike and/or price for a particular time and location. The processing logic may obtain point-of-prediction feature values to be used to predict spike and/or price for the particular time and location as indicated in the request. 
         [0088]    At block  245 , the processing logic may predict a price spike. To predict the price spike, the processing logic may use any of the models of blocks  225 ,  230  and  235 . Various methods for predicting a price spike are further described in conjunction with  FIGS. 3-4 . 
         [0089]      FIG. 3  illustrates a flow diagram of another example method  300  of forecasting a spike price of a commodity. The method  300  may begin at block  305 , where processing logic may obtain a predicted probability of a spike from a random forest model output. In at least one embodiment, the random forest model may include a five-minute or hourly random forest model, as further described in conjunction with  FIGS. 1 and 2 . In at least one embodiment, the processing logic may obtain the predicted probability of a spike from a random forest model output based on point-of-prediction feature values. 
         [0090]    At block  310 , the processing logic may determine whether the predicted probability of the spike is greater than a risk tolerance. The risk tolerance may include the spike risk tolerance and spike price threshold information  104  of  FIG. 1 . The processing logic may compare the predicted spike probability with the risk tolerance to determine whether to warn a user of a possible spike. When the predicted probability of the spike is greater than the risk tolerance (e.g., “YES” at block  310 ), the processing logic may determine that a spike is predicted and may modify a trading strategy. In at least one embodiment, the processing logic may send a message to a user indicative of the predicted spike. In at least one embodiment, when detecting a possible spike, the processing logic may refrain from predicting a spike price. In at least one alternative embodiment, when detecting a possible spike, the processing logic may predict a spike price. 
         [0091]    When the predicted probability of the spike is less than the risk tolerance (e.g., “NO” at block  310 ), the processing logic may use the predicted probability of the spike in a quantile regression model. In at least one embodiment, the processing logic may use random forest probability to predict a non-spike price. For example, the processing logic may perform parameterized weighting of quantile regression estimates with random forest prediction. When a target variable is distributed normally, the processing logic may obtain the probability that each quantile model is optimal from a normal distribution and its density function. In at least one embodiment, the processing logic may predict the probability that each quantile model applies to an observation using the predicted probability of the spike obtained from a random forest model, as further described in conjunction with  FIG. 2 . The processing logic may use the random forest prediction to inform the extent to which a Gaussian, or exponential, weighting function may be used over the quantile regression estimates. The random forest spike probability may inform a weighting function that may be used to augment the prediction from each quantile in the quantile regression, and develop probabilistic estimates for the extent to which each quantile model may apply to an observation. An example equation for the predicted price may include: 
         [0000]    
       
         
           
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         [0000]    where f is a piecewise or monotonically increasing function,           is the predicted probability of spike from the random forest model, {circumflex over (Q)} x  is the predicted price value from the quantile x model, x is the quantile number, and μ, σ, λ, α, are tuned constants. 
         [0092]    The weighting function and model inputs may yield one predicted price when the quantile regression point estimates are weighted according to the above equation. When taking the weighting applied to each individual quantile estimate, the predicted probability may also include the following equation: 
         [0000]    
       
         
           
             
               
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         [0000]    where the specific quantile prediction may be accurate for a given observation. 
         [0093]    Quantile regression may provide several models which may apply to an observation. The random forest probability may indicate how to weight each of these quantile models in order to provide a point or probabilistic price prediction. 
         [0094]    At block  325 , the processing logic may obtain a probabilistic or point non-spike price prediction based on the weighted quantile regression estimates. In at least one embodiment, to predict a non-spike probabilistic price estimate, the processing logic may use the random forest predicted probability to parameterize the weighting function over the quantile estimates from quantile regression. 
         [0095]      FIG. 4  illustrates a flow diagram of a further example method  400  of forecasting a spike price of a commodity. The method  400  for point and probabilistic price prediction may use probability predictions from a random forest model trained to predict the probability that each quantile estimate applies to an observation. The method  400  may begin at block  405 , where processing logic may obtain quantile model estimates for one or more training observations. The training observations may be taken as part of the training as further described in conjunction with  FIG. 2 . 
         [0096]    At block  410 , the processing logic may calculate which quantile model estimate may be closest for each observation. At block  415 , the processing logic may train a random forest model on the resulting dataset of features, with the closest quantile model as the predicted value. The processing logic may predict the probability that each quantile model applies to an observation using the probability that a specific quantile estimate is best according to a random forest model. The random forest model may provide probabilities for a probabilistic estimate of the price, as well as a weight to apply to each quantile model estimate to obtain one point price prediction. 
         [0097]    At block  420 , the processing logic may provide the point-of-prediction feature values into the quantile regression models. The processing logic may obtain a price estimate from each quantile regression model based on the point-of-prediction feature values provided to the quantile regression models. 
         [0098]    At block  425 , the processing logic may obtain a probability that each quantile estimate may apply from the random forest model. At block  430 , the processing logic may obtain an estimate and probability for probabilistic price forecasting. In some alternative embodiments, the processing logic may multiply and/or sum the probability that each quantile estimate may apply from the random forest model and the price estimate from each quantile regression model to obtain a predicted price. An example equation for the predicted price may include: 
         [0000]    
       
         
           
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         [0000]    where           is the predicted probability that each quantile model applies (from the random forest model), {circumflex over (Q)} x  is the predicted price value from the quantile x model, and x is the quantile number. 
         [0099]    At block  435 , the processing logic may report a spike when the predicted price is above a price spike threshold or may report a non-spike when the predicted price is below a price spike threshold. 
         [0100]      FIGS. 5A and 5B  illustrate various example visualization outputs of predicted spike and price.  FIG. 5A  illustrates an example visualization output  500  of an actual past price (illustrated as a black line and by region  505 ) for one day and a one-hour-ahead price prediction, which is illustrated as the dotted line and also indicated in region  510 . A prediction of a probability of a spike is illustrated as different fill patterns to indicate different probability ranges: Level 0, Level 1, Level 2, and Level 3. As illustrated, a probability of a spike increases with each level such that Level 0 indicates a lower spike probability and Level 3 indicates a higher spike probability. 
         [0101]      FIG. 5B  illustrates another example visualization output  550  of a location-specific forecast of price spike likelihood. As illustrated, the visualization output  550  includes a geographic region  555  that is divided into subdivisions. The price spike likelihood is illustrated as different fill patterns to indicate different probability ranges: Low, Medium, and High. As illustrated, a probability of a probability of a spike increases with each level such that Low indicates a lower spike probability and High indicates a higher spike probability. 
         [0102]      FIG. 6  is a block diagram illustrating an example computing device  600  that is arranged for probabilistic price and spike forecasting, arranged in accordance with at least one embodiment described herein. In a basic configuration  602 , the computing device  600  typically includes one or more processors  604  and a system memory  606 . A memory bus  608  may be used to communicate between the processor  604  and the system memory  606 . 
         [0103]    Depending on the desired configuration, the processor  604  may be of any type including, but not limited to, a microprocessor (μP), a microcontroller (μC), a digital signal processor (DSP), or any combination thereof. The processor  604  may include one or more levels of caching, such as a level one cache  610  and a level two cache  612 , a processor core  614 , and registers  616 . The processor core  614  may include an arithmetic logic unit (ALU), a floating point unit (FPU), a digital signal processing core (DSP Core), or any combination thereof. An example memory controller  618  may also be used with the processor  604 , or in some implementations the memory controller  618  may be an internal part of the processor  604 . 
         [0104]    Depending on the desired configuration, the system memory  606  may be of any type including, but not limited to, volatile memory (such as RAM), nonvolatile memory (such as ROM, flash memory, etc.), or any combination thereof. The system memory  606  may include an operating system  620 , one or more applications  622 , and program data  624 . The application  622  may include an input feature selection algorithm  626  that is arranged to perform input feature selection as is described herein. The program data  624  may include input feature data  628  as is described herein, or other input feature data. In some embodiments, the application  622  may be arranged to operate with the program data  624  on the operating system  620  such that the methods  200 ,  300 , and  400  of  FIGS. 2, 3, and 4 , respectively, may be provided as described herein. 
         [0105]    The computing device  600  may have additional features or functionality, and additional interfaces to facilitate communications between the basic configuration  602  and any involved devices and interfaces. For example, a bus/interface controller  630  may be used to facilitate communications between the basic configuration  602  and one or more data storage devices  632  via a storage interface bus  634 . The data storage devices  632  may be removable storage devices  636 , non-removable storage devices  638 , or a combination thereof. Examples of removable storage and non-removable storage devices include magnetic disk devices such as flexible disk drives and hard-disk drives (HDDs), optical disk drives such as compact disk (CD) drives or digital versatile disk (DVD) drives, solid state drives (SSDs), and tape drives to name a few. Example computer storage media may include volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information, such as computer-readable instructions, data structures, program modules, or other data. 
         [0106]    The system memory  606 , the removable storage devices  636 , and the non-removable storage devices  638  are examples of computer storage media or non-transitory computer-readable medium or media. Computer storage media or non-transitory computer-readable media includes RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVDs) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which may be used to store the desired information and which may be accessed by the computing device  600 . Any such computer storage media or non-transitory computer-readable media may be part of the computing device  600 . 
         [0107]    The computing device  600  may also include an interface bus  640  to facilitate communication from various interface devices (e.g., output devices  642 , peripheral interfaces  644 , and communication devices  646 ) to the basic configuration  602  via the bus/interface controller  630 . The output devices  642  include a graphics processing unit  648  and an audio processing unit  650 , which may be configured to communicate to various external devices such as a display or speakers via one or more A/V ports  652 . The peripheral interfaces  644  include a serial interface controller  654  or a parallel interface controller  656 , which may be configured to communicate with external devices such as input devices (e.g., keyboard, mouse, pen, voice input device, touch input device, etc.), sensors, or other peripheral devices (e.g., printer, scanner, etc.) via one or more I/O ports  658 . The communication devices  646  include a network controller  660 , which may be arranged to facilitate communications with one or more other computing devices  662  over a network communication link via one or more communication ports  664 . 
         [0108]    The network communication link may be one example of a communication media. Communication media may typically be embodied by computer-readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave or other transport mechanism, and may include any information delivery media. A “modulated data signal” may be a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media may include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, radio frequency (RF), microwave, infrared (IR), and other wireless media. The term “computer-readable media” as used herein may include both storage media and communication media. 
         [0109]    The computing device  600  may be implemented as a portion of a small-form factor portable (or mobile) electronic device such as a smartphone, a personal data assistant (PDA), or an application-specific device. The computing device  600  may also be implemented as a personal computer including both laptop computer and non-laptop computer configurations, or a server computer including both rack-mounted server computer and blade server computer configurations. 
         [0110]    Embodiments described herein may be implemented using computer-readable media for carrying or having computer-executable instructions or data structures stored thereon. Such computer-readable media may be any available media that may be accessed by a general-purpose or special-purpose computer. By way of example, and not limitation, such computer-readable media may include non-transitory computer-readable storage media including Random Access Memory (RAM), Read-Only Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-Only Memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid state memory devices), or any other storage medium which may be used to carry or store desired program code in the form of computer-executable instructions or data structures and which may be accessed by a general-purpose or special-purpose computer. Combinations of the above may also be included within the scope of computer-readable media. 
         [0111]    One skilled in the art will appreciate that, for this and other processes and methods disclosed herein, the functions performed in the processes and methods may be implemented in differing order. Further, the outlined steps and operations are only provided as examples, and some of the steps and operations may be optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments. 
         [0112]    Computer-executable instructions may include, for example, instructions and data which cause a general-purpose computer, special-purpose computer, or special-purpose processing device (e.g., one or more processors) to perform a certain function or group of functions. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims. 
         [0113]    As used herein, the terms “module” or “component” may refer to specific hardware implementations configured to perform the operations of the module or component and/or software objects or software routines that may be stored on and/or executed by general-purpose hardware (e.g., computer-readable media, processing devices, etc.) of the computing system. In some embodiments, the different components, modules, engines, and services described herein may be implemented as objects or processes that execute on the computing system (e.g., as separate threads). While some of the system and methods described herein are generally described as being implemented in software (stored on and/or executed by general-purpose hardware), specific hardware implementations or a combination of software and specific hardware implementations are also possible and contemplated. In this description, a “computing entity” may be any computing system as previously defined herein, or any module or combination of modulates running on a computing system. 
         [0114]    All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Although embodiments of the present inventions have been described in detail, various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.