Autoregressive and Moving Average Model (ARMA)

We all know that financial data analysis cannot do without such a stage as forecasting. After various checks and tests, studying the main patterns and recommendations, you need to make a forecast. What to do when analyzing data such as a time series. As a rule, the first thing you need is visual perception. After proceeding with the selection of a model for forecasting.

In this article, we will look at the ARMA (Autoregressive moving average) model. This is a mathematical model that is used to analyze and predict stationary series in statistics. ARMA combines simple time series models: autoregression (AR) and moving average (MA). So, it is formula of a stationary process:

Where ε – white noise, с — constant.

A total of q previous values of ε. And we assume that the sum p + q is the smallest possible.

The model is designated as ARMA (p, q), the first parameter p is the number of lags for autoregression (AR), and q is the number of lags for the moving average (MA).

ARMA processes are just about everything you need to know about stationary processes. There is a theorem that says any stationary process can be represented as autoregression with an infinite number of lags. In ARMA process, you can choose p, q large enough and choose the coefficient before wye and before epsilons in such a way as to approximate the predicted values ​​with the actual ones. Therefore, the ARMA (p, q) model is sufficient to explain any stationary process.

It must be remembered that the coefficients of the ARMA model are not interpretable, but despite this they are successfully used in forecasting.

The algorithm for constructing the ARMA model (p, q):

  1. We are building a graph of a series, graphs of autocorrelation function. This study will help describe the characterization of the series.
  2. Determine the stationarity of the series, if the series is non-stationary, then you need to convert to make the series stationary. We will write about this in the next article.
  3. Select the model parameters (the number of lags of models AR and MA).
  4. Assessment of the model.
  5. We use.

Since these processes are algorithmized, we can use this to create a macro in Caseware IDEA, , as it is simple. The first time to evaluate any routine process and then use this model in forecasting client or your own data.

In the next article, we will consider ARIMA processes and show in practice how to create a model for forecasting time series.

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