Time Series Analysis

DATA BRIO ACADEMY

TIME SERIES ANALYSIS What is a Time Series?

Databrio 2/18/2016

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When we have a chronologic chronologically ally ordered collection (set) of data points, we refer to the data set as time series. So, a time series is a sequence of observations taken sequentially in time series data can have both univariate and multivariate quantitative data collected over time.

For example, let us say that we have the attrition rate data of a company for the past 12 months. The senior manager wants to know the probable attrition rate for the 13 th and 14th month, so that he can prepare his current workforce and initiate any recruitment process if necessary. As we have the data points arranged chronologically, we say that the data is a time series data.. For predicting the probable attrition rate for any future period, we data have to use time series analysis which has been discussed below. belo w.

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There are two classes of time series process: Stationary and Non-Stationary So, what is stationarity? Covariance stationarity follows three conditions-

1) Unconditional mean and variance should be constant

E(Yt) = E(Yt+j) = µ Var (Yt) = Var(Yt+j)=σ 2

2) Covariance depends on time j that has elapsed between observations, not on reference period.

Cov(Yt,Yt+j) = Cov(Ys,Ys+j) = γ Any time series data which data which follows the above mentioned conditions are known as stationary time series. Similarly, if a time series data do not conform to the above conditions, they are termed as non-stationary time series data. For a non-stationary time series, the mean, variance and the covariance changes. There is no long-run mean to which the series returns. Also, the variance is tie-dependent,, for eg., it could go to infinity as the number of observation tie-dependent goes to infinity. Unit root tests are used to find out non-stationary time series. One of the commonly used tests for non-stationarity is the “Dickey Fuller” test. Other

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The process flow for time-series analysis is as follows:

At first, using unit root tests find out whether the time series is stationary or not. If it is stationary, proceed proceed to find out the best ARMA model using different diagnostic tests. After selecting the best suited model, forecast for future periods and again use different diagnostic tests to find out how good the forecast is. If in case the unit root test like “Dickey-Fuller” test shows the time series to

be non-stationary, then you have to transform the data into stationary series. Differencing is widely used to transform the data into stationary series. Once, the data is transformed into stationary time series, follow the previous steps to forecast the model.

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Stationary Process:

After identification of a stationary time series process, estimation and model selection is done. Stationary Process can be of three basic types: 1. Autoregressive(AR)Autoregressive(AR)-It It means that the variable is a function of its own lagged values upto a maximum lag of p. 2. Moving Average(MA)-It means the variable is a function of the disturbances upto a maximum lag of q. 3. Combined(ARMA Combined(ARMA)-It )-It includes both the elements, i.e. have lagged values of the variable and lagged values of the disturbance.

So, for estimation of time series and model selection, decide whether the time series is a pure AR/ MA or ARMA process. Then estimate the specifications like auto-covariance, auto-correlation and partial auto- correlation. Finally, choose Finally,  choose the best model based model  based on the significance of coefficients, white noise residuals, fit vs parsimony and ability to forecast.

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