The Complete Guide to Time Series Models.
Tags: beginners, data, datascience
Published: 2023-10-27 18:57:56

Time series data is everywhere in our lives. It can be found in almost any domain: monitoring, sensors, stock prices, weather forecasts, exchange rates, application performance, and a plethora of other metrics on which we rely in our professional and personal life.

## What is time series data?
Time-series analysis refers to the technique and mathematical tools used to examine time-series data in order to discover not only what happened but also when and why it happened, as well as what is most likely to happen in the future.

## ‌‌Types of Time-Series Analysis

- **Exploratory analysis**
When you wish to describe what you observe and why you see it in a given time series, an exploratory analysis can help. It requires breaking down the data into trends, seasonality, cyclicity, and abnormalities. ‌‌
We can explain what each component symbolizes in the real world and, maybe, what caused it once the series has been deconstructed. This is not as simple as it appears and frequently involves spectrum decomposition to identify any specific frequency of recurrences and autocorrelation analysis to determine whether present values are dependent on prior values.

- **Curve fitting**
Because time series is a discrete set, you can always tell how many data points are in it.
But what if you want to know the value of a time-series parameter at a point in time that your data does not cover? 

To address this question, we need to add a continuous set—a curve—to our data. This can be accomplished in a variety of methods, including interpolation and regression. The former is a perfect match for parts of the given time series and is mostly useful for guessing missing data points. The latter, on the other hand, is a "best-fit" curve, which requires you to make an informed guess about the form of the function to be fitted (e.g., linear) and then modify the parameters until your best-fit criteria are met. 

- **Forecasting**
The process of generalization from sample to whole is known as statistical inference. It can be done over time with time-series data, allowing for future predictions or forecasting: from extrapolating regression models to more complex techniques involving stochastic simulations and machine learning.

- **Classification and segmentation**
Classification is the process of identifying patterns in a series and assigning them to one of several classes. Segmentation, on the other hand, is the process of dividing a time series into a number of segments based on some specified criterion. ‌‌‌‌‌‌

## Time series data visualization
Time series data visualization is often conducted with specialist tools that offer users a variety of visualization kinds and formats from which to pick. Let's look at some of the most popular data visualization methods.

- **Time series graph**
Time series graphs, also known as time series plots, are the most commonly used data visualization tool for illustrating data points at a temporal scale where each point corresponds to both time and the unit of measurement.

- **Real time graph**
Time series data is displayed in real time using real time graphs, often known as data streaming charts. This means that a real-time graph will refresh automatically every few seconds or when a new data point is received from the server.

## Data models used for time series data

- **Autoregressive (AR) models**

AR model is a representation of a form of random process, it is used to describe data reflecting time-varying processes such as changes in weather, economics, and so on.

- **Integrated (I) models**

Integrated models are made up of a series of random walk components. These series are called integrated because they are the summation of weakly steady components.

- **Moving-average (MA) models**

Univariate time series are modeled using moving-average models. The output variable in MA models is linearly dependent on the current and various historical values of an imperfectly predicted (stochastic) factor.

- **Autoregressive moving average (ARMA) models**

ARMA models combine the AR and MA classes, with the AR part regressing the variable on its own historical values and the MA part modeling the error term as a linear mixture of error terms happening concurrently and at different times in the past. ARMA models are commonly employed in analytics for forecasting future values in a series.

- **Autoregressive integrated moving average (ARIMA) models**

ARIMA models are a generalization of an ARMA model and are used when data show evidence of non-stationarity, where an initial differencing step, corresponding to the integrated part of the model, can be applied one or more times to eliminate the mean function's non-stationarity.

Both the ARMA and ARIMA models are commonly employed for analytics and forecasting future values in a series.

- **Autoregressive fractionally integrated moving average (ARFIMA)**

ARFIMA models, in turn, generalize ARIMA models (or, more broadly, all three fundamental types) by allowing non-integer differencing parameter values. ARFIMA models are commonly used to simulate so-called long memory time series, in which deviations from the long-run mean dissipate more slowly than exponential decay.

- **Autoregressive conditional heteroscedasticity (ARCH)**

The ARCH model, for example, describes the variance of the present error term or innovation as a function of the actual sizes of error terms in earlier time periods.

## Challenges in Handling Time-Series Data
While time series data provides great insights, it also brings distinct obstacles that must be handled during analysis.

- **Dealing with missing values**
Time-series data frequently contains missing or partial values, which can impair analysis and modeling accuracy. Depending on the nature of the data and the level of missing values, several techniques such as interpolation or imputation can be used to handle missing values.

- **Overcoming noise in time-series data**
Noise in time series data refers to random fluctuations or anomalies that can conceal underlying patterns and trends. Moving averages and wavelet treatments, for example, can assist minimize noise and extract the most important information from data.

In conclusion, time series analysis attempts to understand how patterns develop over time. These patterns aid in the generation of exact estimates for things like future sales, GDP, and global temperatures.
One thing to keep in mind is that time series models take into account the fact that time flows in only one direction.
Events that are near in time often have a greater link than more distant discoveries.
Time-series data, like all data, has random oscillations. This randomness has the potential to hide the underlying patterns. Smoothing techniques help to wipe out these swings, revealing the trends and cycles more clearly.
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