Time Series - Modeling

Introduction

A time series has 4 components as given below −

• Level − It is the mean value around which the series varies.

• Trend − It is the increasing or decreasing behavior of a variable with time.

• Seasonality − It is the cyclic behavior of time series.

• Noise − It is the error in the observations added due to environmental factors.

Time Series Modeling Techniques

To capture these components, there are a number of popular time series modelling techniques. This section gives a brief introduction of each technique, however we will discuss about them in detail in the upcoming chapters −

Naïve Methods

These are simple estimation techniques, such as the predicted value is given the value equal to mean of preceding values of the time dependent variable, or previous actual value. These are used for comparison with sophisticated modelling techniques.

Auto Regression

Auto regression predicts the values of future time periods as a function of values at previous time periods. Predictions of auto regression may fit the data better than that of naïve methods, but it may not be able to account for seasonality.

ARIMA Model

An auto-regressive integrated moving-average models the value of a variable as a linear function of previous values and residual errors at previous time steps of a stationary timeseries. However, the real world data may be non-stationary and have seasonality, thus Seasonal-ARIMA and Fractional-ARIMA were developed. ARIMA works on univariate time series, to handle multiple variables VARIMA was introduced.

Exponential Smoothing

It models the value of a variable as an exponential weighted linear function of previous values. This statistical model can handle trend and seasonality as well.

LSTM

Long Short-Term Memory model (LSTM) is a recurrent neural network which is used for time series to account for long term dependencies. It can be trained with large amount of data to capture the trends in multi-variate time series.

The said modelling techniques are used for time series regression. In the coming chapters, let us now explore all these one by one.