MULTI-LOCATIONAL FORECAST MODELING IN BOTH TEMPORAL AND SPATIAL DIMENSIONS

Temporal and spatially integrated forecast modeling includes generating a plurality of forecast models for a plurality of short-term to long-term time periods for a plurality of locations. Temporally integrating the plurality of forecast models sequentially over the plurality of time periods for the plurality of locations and spatially integrating the temporally integrated plurality of forecast models for each location hierarchically over the geographic areas. The forecast models are autoregressive distributed lag models with different explanatory variables for the short-term and long-term forecast models. The temporally integrating includes recursively integrating the plurality of forecast models over the time periods from the short-term to the long-term time periods and the spatially integrating includes recursively integrating the temporally integrated plurality of forecast models hierarchically from larger size geographic areas to smaller size geographic areas. The method includes optimizing the resultant spatially and temporally integrated forecast model based on a plurality of constraints.

BACKGROUND

This disclosure is directed to forecast modeling, and more particularly to computers, computer applications, and computer-implemented methods and systems for multi-locational forecasting in both temporal and spatial dimensions.

Both long-term and short term forecasting is needed to forecast market conditions in many industries such as commercial and residential real estate and global supply chain network investment. For example, real estate investment strategies need a forecast on the long-term capital return. Long term forecasting needs at least five years to be useful, however, market performance will be very different in different years, particularly if there is an economy cycle involved. For example, construction typically needs at least a two to three year forecast that considers risks and opportunities with long construction lead-times in multiple locations.

Short-term forecasting is also needed for either strategic or operations decisions. Timing of the breaking/turning point of an economy cycle or impact of natural disasters must be considered for annual operational decisions. Some signals/variables that are useful in the short term forecast may not be statistically significant in the long-term forecast. Some simple forecasting models such as ARIMA, in which the forecasting horizon can be easily extended in a rolling manner, cannot provide an accurate forecast in most of the industries, because both short and long term forecasts are based on the same set of autoregressive variables.

Geographical location is also important as local forecasts will impact the investment portfolio management. Market performance is highly differentiated in local markets. For example, there may be positive returns in a few locations even in a year in which returns in most areas are down.

Funding availability will dynamically change in terms of short-term returns and become a constraint of long-term investment. However, Current forecasting models do not provide optimization based on the consistent forecasting results in both temporal and spatial dimensions.

SUMMARY

One embodiment of a computer implemented method for forecast modeling includes the step of generating a plurality of forecast models for a plurality of time periods, in which the time periods include short-term and long-term time periods. Each forecast model of the plurality of forecast models is for a different time period for a plurality of locations. The locations include a plurality of geographic areas grouped hierarchically based the geographic size of the areas. The method further includes temporally integrating the plurality of forecast models sequentially over the plurality of time periods for the plurality of locations and spatially integrating the temporally integrated plurality of forecast models for each location hierarchically over the geographic areas to generate a resultant spatially and temporally integrated forecast model.

In one embodiment, the plurality of forecast models are generated based on a set of variables in a general forecasting model, such as an autoregressive distributed lag model (ARDL), which may have different explanatory variables for the short-term forecast models and for the long-term forecast models. In one embodiment, the temporally integrating includes recursively integrating the plurality of forecast models over the time periods from the short-term to the long-term time periods. In one embodiment, the spatially integrating includes recursively integrating the temporally integrated plurality of forecast models hierarchically from larger size geographic areas to smaller size geographic areas. In one embodiment, the method includes optimizing the resultant spatially and temporally integrated forecast model based on a plurality of constraints.

A computer system that includes one or more processors operable to perform one or more methods described herein also may be provided.

DETAILED DESCRIPTION

In one embodiment, a forecast modeling system and method is disclosed that integrates forecast models along the temporal dimension, such as for a plurality of time periods extending from the short-term to the long-term and integrates the temporally integrated forecast models across the spatial dimension, such as hierarchically over a plurality of geographic locations, for example, local, regional, national and global, to generate a resultant spatially and temporally integrated forecast model. The resultant spatially and temporally integrated forecast model is a forecast for the plurality of locations in the plurality of time periods.

FIG.1is a flow diagram of one embodiment of a method of forecast modeling that includes step S10of generating a plurality of forecast models for a plurality of time periods. The time periods include both short-term and long-term time periods. In one embodiment, each forecast model of the plurality of forecast models is for a different time period for a plurality of geographic locations that include a plurality of regions that are hierarchically defined based the geographic size of the regions.

Step S12includes temporally integrating the plurality of forecast models sequentially from a short-term to a long-term time period for the plurality of geographic locations. In one embodiment, the temporal forecasting models are integrated in a nested manner such that the short-term forecasting output can be used as an input into the mid-term forecast model, and the mid-term forecast model is used as input to the long-term forecast model, in order to gauge the forecasting results along the temporal dimension.

Step S14includes spatially integrating the temporally integrated plurality of forecast models for each geographic location hierarchically over the regions to generate a resultant spatially and temporally integrated forecast model.

In one embodiment, in the spatial dimension, weights are assigned in a hierarchical way from global to national to regional to local areas. In one embodiment, the hierarchical integration is performed in the spatial dimension iteratively. In one embodiment, grouping the locations such as cities and regions hierarchically may enable a segmentation analysis.

The resultant spatially and temporally integrated forecast model generates forecasting results in both the temporal and spatial dimension thereby providing consistent forecasts for all of the plurality of geographic locations for each of the time periods. For example, the resultant spatially and temporally integrated forecast model may predict long, median and short term investment gain periods for different geographical regions. Because the integration of forecasting models takes place in both spatial and temporal dimension, the resultant spatially and temporally integrated forecast model can be applied to study the long-term investments in multiple locations and thereby optimize portfolio gains across multiple locations. Therefore, the resultant spatially and temporally integrated forecast model provides a consistent forecast across different time scale and geographic scope. In one embodiment, the resultant spatially and temporally integrated forecast model provides consistency in the temporal dimension and in the spatial dimension with different sets of explanatory variables in each dimension using autoregressive distributed lag models.

In one embodiment, the resultant spatially and temporally integrated forecast model can provide real-time feedback by automatically synchronizing all the forecast results in the spatial and temporal dimensions, so that if any forecast changes in any level from short-term to long-term, from local to global, the resultant spatially and temporally integrated forecast model will reflect such changes. For example, changes may occur due to regular update of the sensors data or a planned event, while some unscheduled events will affect the long-term and some may not. Therefore, the resultant spatially and temporally integrated forecast model results may provide both the expected return and the risks correspondingly.

In one embodiment, the resultant spatially and temporally integrated forecast model can optimize the decisions in time and also across multiple locations. In one embodiment, dynamic portfolio optimization takes into account various constraints, such as, the constraints of funding and construction lead-times in real estate investment, whereas the prior art forecast models do not take into account such constraints and concerns. Step S16inFIG.1is an optional step for optimizing the resultant spatially and temporally integrated forecast model based on a plurality of constraints.

In one embodiment, the resultant spatially and temporally integrated forecast model continues to optimize the investment portfolio based on the integrated forecasting results in a spatio-temporal network over time. In one embodiment, an optimization system to support the real-estate investment, based on the resultant spatially and temporally integrated forecast model for a portfolio of investment strategies, may include leasing, joint venture, ownership, etc. The optimized resultant spatially and temporally integrated forecast model will provide balancing of the short-term and long-term returns together with forecasted revenue flow along the timeline and balancing the returns and risks across multiple locations.

In one embodiment, the resultant spatially and temporally integrated forecast model can provide capital gain forecasting that allows for strategic investment over a business cycle, which is an improvement over the prior art models that provide demand forecasting of short-term revenue/profit optimization.

In one embodiment, the resultant spatially and temporally integrated forecast model provides dynamic portfolio optimization integrated with revenue forecast across multiple periods so that the expected revenue will regulate the funding available to investment. For example, an event such as the pandemic may strongly limit the investment in an industry in the short-term. Portfolio optimization using the resultant spatially and temporally integrated forecast model under the constraints of funding and lead-time will determine the future revenue. Short-term forecast will foresee the expected funding in the near future and thereby the size of portfolio. In turn, the expected funding will affect the overall capital return in the long-term. Thus, the resultant spatially and temporally integrated forecast model provides portfolio optimization with multiple options in a geographic network.

FIG.2is a block diagram of one embodiment of a forecast modeling system10for implementing the method of integrating forecasting models in both spatial and temporal dimensions. The modeling system10includes a long-term forecasting model12and a short-term forecasting model14. The long-term forecasting model12generates a plurality of forecast models for a plurality of long-term time periods such as, for example, four to five years for a plurality of geographic locations, the geographic locations including a plurality of regions defined hierarchically based the geographic size of the regions. The short-term forecasting model14generates a plurality of forecast models for a plurality of short-term time periods such as, for example, one to three years for the plurality of geographic locations.

Integration module16temporally integrates the plurality of long-term and short-term forecast models12and14sequentially over the plurality of time periods for the plurality of geographic locations. For example, the forecast models12and14may be integrated from short-term to long-term, such as from year one to year five. The integration module16then spatially integrates the temporally integrated plurality of forecast models for each geographic location hierarchically over the regions to generate a resultant spatially and temporally integrated forecast model. For example, the temporally integrated plurality of forecast models may be integrated from larger to smaller regions, such as, state to city to county, or nation to state to city.

Dynamic portfolio optimization module18applies constraints to the resultant spatially and temporally integrated forecast model for optimizing decisions using on the integrated forecast model. In module20, the results of the spatially and temporally integrated forecast model are analyzed and displayed to the user. Optimization module18is an optional module as results of the spatially and temporally integrated forecast model may be directly displayed from module16.

The forecast modeling system10includes database22that stores information input to the long-term and short-term forecasting models12and14. For example, in one embodiment for forecasting for real estate investment decisions, the input data may include historical compound annual growth rate (CAGR)24, city demand (e.g., tourists, migration, etc.)26, city supply (e.g., construction, etc.)28, and social and economy data30that may include macro and micro economy data. Also stored in database22are available opportunities32(e.g., land price, etc.).

In one embodiment, inputs for optimization module18may include cash flow and debt/loans data obtained from corporate finance data36and cost analysis data38of the available opportunities32. Cost analysis data38may include cost of existing projects. Investment regulations may also be input as the constraints to optimization module18.

The data stored in database22is input to segmentation module42. In segmentation module42, the locations from which the data stored in database22is obtained from includes a plurality of locations that include a plurality of geographic areas grouped hierarchically based the geographic size of the areas. For example, the hierarchical grouping of areas in the United States may include cities and regions such as a state and the nation. The hierarchical grouping allows for the spatial integration of the forecasting models and enables segmentation analysis of the results. In one embodiment, the cash flows and debts data34is also input to the segmentation module42where the land cost can be used as an attribute to enhance the segmentation analysis.

The segmented data from module42is input to modules44and46. Module44formulates and determines the variables for the long-term forecast model12and module46formulates and determines the variables for the short-term forecast model14. In one embodiment the short-term and long-term forecast models12and14are autoregressive distributed lag (ARDL) models. A distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable.

Below is shown the equations for an ADL model to forecast CAGR, where Y is the dependent variable CAGR and X1to Xnare the explanatory variables.

1-year CAGR forecast at the end of time period t, in any location i:

2-year CAGR forecast at the end of time period t, in any location i:

τ-year CAGR forecast at the end of time period t, in any location i:

Location is indexed by i, for any nation/region/city, in the superscript of any variable. Time is indexed by t, in the subscript of any variable. Autoregressive variables may have different time lags (l1≠l2≠ . . . ≠lT), where T is the maximum period. The number of explanatory variables (X) used in τ-year forecast is denoted by nτ, for τ=1, . . . , T. Different set of explanatory variables may be used from short-term and the long-term models (n1≠ . . . ≠nT). These models [0035] are independent and may give inconsistent forecasting results along the timeline. Consider a booming phase of economy, a one-year forecasting model may predict a 3% growth next year, and a two-year model may predict a 2% growth in the next two year. Such results mean an approximately 1% decline in the second year, which contradicts with the economic booming phase.

For example, the historical CAGR24may have different time lags for the short-term and long-term models. The social-economy data30may also have various time lags for the short-term and long-term models.

FIG.3is a table showing of one example of the number and types of explanatory variables X that can be determined from the historical CAGR data24, city demand data26, city supplies data28and the social-economy data30.

Prior art forecasts along temporal dimension would have results as follows:

Example of inconsistent CAGR forecast:1-yr2-yr3-yr4-yrAtlanta2.3%2.1%2.0%−0.1%Jacksonville1.9%2.0%2.0%1.4%

Reasons for the inconsistent results may be cities may be in different segments where the regression coefficients are very different or different variable sets are used in the forecast of different time horizons (1-yr, 2-yr, etc.).

The integration module16integrates the forecast in a recursive way along the temporal dimension. Compared to the independent forecasting models in [0035], here, the 1-year forecast result becomes an explanatory variable in the 2-year forecast. Therefore, the forecasting models are formulated in a nested way, for example, from short to long time horizon as shown by the equations below:

1-year CAGR forecast at time t, in any location i:

2-year CAGR forecast at time t, in any location i:

τ-year CAGR forecast at time t, in any location i:

Prior art forecasts are also inconsistent in spatial dimension.

The reasons may be the regression models of national/regional forecasts are different from those of local forecasts and data history is typically longer in the national statistics than many locals.

Integration module16integrates forecast in a recursive way in the spatial dimension. Compared to the independent forecasting models in [0035], here, the t-year forecast result of a nation 0 becomes an explanatory variable in the τ-year forecast of any sub regions r. Similarly, the τ-year forecast result of any region r becomes an explanatory variable in the τ-year forecast of any of its sub regions i. Therefore, the forecasting models are formulated in a nested way, for example, top-down in the spatial dimension.

τ-year CAGR forecast in a nation indexed by 0:

τ-year CAGR forecast in each region indexed by r:

τ-year CAGR forecast in each local city indexed by i∈r:

FIG.4is a table showing an example output of module16of the resultant spatially and temporally integrated forecast model for CAGR forecast in the future 1-5 years for 9 cities in 2 regions. In one embodiment, the resultant spatially and temporally integrated forecast model can be denoted by a sequence of vectors: {right arrow over (Y)}t+1, . . . , {right arrow over (Y)}t+T

{right arrow over (Y)}t+τis a vector of τ-year forecast for 9 cities.

In one embodiment, a standard error of forecast can also be presented in a similar table toFIG.4. The distribution of forecast errors can be tested and verified accordingly

The optimization module18determines and applies variables for optimization of the forecast output result from module16.

{right arrow over (Y)}t+1, . . . , {right arrow over (Y)}t+T: is an example of the temporally and spatially integrated forecast for all the cities in the future T years input to module18. Real market returns can be regarded as random variables around the forecast values.

Also input to module18may be decision variables and state variables. For example, in one embodiment:

zt+1⊆At: new lands selected from the set of available lands at the end of period t, denoted by At
Zt: existing portfolio (lands under investment) at the end of period t−1
Mt: net income in period t
{right arrow over (B)}t=(Bt,ξt, . . . , B0,ξ0), where Bt,ξtis the money borrowed in t and will be return after ξtperiods.

Dynamics or changes in the variables from period t to t+1 may be represented as:

Rt+1(Zt;{right arrow over (Y)}t+1) is the expected revenue generated by the existing lands Ztbased on the forecast {right arrow over (Y)}t+1
Ct+1(zt+1,Zt,{right arrow over (B)}t) is the cost of investment zt+1, Ztand pay for the money borrowings {right arrow over (B)}t

Matured date ξt+1for Bt+1will be selected to minimize the overall interests

In one embodiment, the objective function Vt(z;Zt,Mt,{right arrow over (B)}t) is total expected return after period t (from t+1 to t+T), for any new investment z.

The dynamic portfolio optimization module18will optimize the integrated forecast model to maximize total expected returns based on the decision and state variables as follows:

η is a time discount rate;
Vt+1*(Zt+1,Mt+1,{right arrow over (B)}t+1) is the maximum total expected returns after period t+1 (from t+2 to t+T);
Rt+1(Zt;{right arrow over (Y)}t+1) is the revenue based on the existing lands Ztand market returns {right arrow over (Y)}t+1at the end of period C;
Ct+1(zt+1,Zt,{right arrow over (B)}t) is the cost based on the investment zt+1, Ztand money borrowings {right arrow over (B)}t=(Bt, . . . , B0).
The optimization module18will also apply constraints. In one embodiment, the constraints may include: zt+1∈Atand

Bt+1=max{0,Ct+1(zt+1,Zt,{right arrow over (B)}t)−E{right arrow over (Y)}t+1Rt+1(Zt;{right arrow over (Y)}t+1)−Mt}.

If the available cash is more than the cost of investment and debt, then no loan is needed, that is Bt+1=0.
The constraints may also include:

FIG.5is a graph showing an example of the dynamics of the spatio-temporal investment decisions that can be made using the temporally and spatially integrated forecast model output from module16and optimized by module18. There are three locations indexed by L1, L2 and L3 in the example. The current year is indexed by Y0 with historical data in the past three years indexed by Y−1, Y−2 and Y−3 respectively. The forecast is laid out in the next 5 years, indexed by Y1, Y2, . . . , Y5. The height of the bars in each year shows the return of investment, where all the bars in years Y−2 and Y−1 are a negative return and the bars in years Y−3 and Y0-Y5 are a positive return. The returns in years Y−3, Y−2 and Y−1 were based on historical data whereas the returns in years Y0-Y5 are from the forecasting results. The recession R started two years ago (indexed by Y−2). At that moment, the investment I1was made in land 3, since it seemed to recover quicker than land 1 and 2 immediately after the recession. Such construction needs 3 years, so continuous investment I2and I3were made in years Y0 and Y1 and the return ROI will start after 2 years (in Y2). It seems that Y0 may not be a good year to invest, given a very tight budget due to the recession in the past two years and a project of land 3 right on the way. A decision maker needs to consider if any investment I4will go to location 1 and 2 in the coming year (Y1). The forecasting results show a good timing to invest location 1 in Y1, since a stronger return will come in Y4 and Y5 than that of location 2 based on the long-term forecast. Also, the firm's financial pressure of continuous investment I5and I6may not be tight in the years of Y2 and Y3, because an expected strong returns of location 1 will come in these years based on the short-term forecast.

The components of computer system may include, but are not limited to, one or more processors or processing units100, a system memory106, and a bus104that couples various system components including system memory106to processor100. The processor100may include a program module102that performs the methods described herein. The module102may be programmed into the integrated circuits of the processor100, or loaded from memory106, storage device108, or network114or combinations thereof.

Computer system may also communicate with one or more external devices116such as a keyboard, a pointing device, a display118, etc.; one or more devices that enable a user to interact with computer system; and/or any devices (e.g., network card, modem, etc.) that enable computer system to communicate with one or more other computing devices. Such communication can occur via Input/Output (I/O) interfaces110.

Still yet, computer system can communicate with one or more networks114such as a local area network (LAN), a general wide area network (WAN), and/or a public network (e.g., the Internet) via network adapter112. As depicted, network adapter112communicates with the other components of computer system via bus104. It should be understood that although not shown, other hardware and/or software components could be used in conjunction with computer system. Examples include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc.