DATA BRIO ACADEMY

TIME SERIES ANALYSIS What is a Time Series?

Databrio 2/18/2016

When we have a chronologically 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 13th 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

have to use time series analysis which has been discussed below.

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) =

Var (Yt) = Var(Yt+j)=2

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

reference period.

Cov(Yt,Yt+j) = Cov(Ys,Ys+j) =

Any time series 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

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

tests include Augmented Dickey-Fuller test and KPSS test.

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 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.

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)-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)-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 the best model based on the significance of coefficients, white

noise residuals, fit vs parsimony and ability to forecast.

CONTACT US :

ADDRESS :

Data Brio Academy 1st Floor, 135/L SP Mukherjee Road,

Near RashBehari Crossing, Lake Range, Kalighat,

Kolkata, West Bengal

PIN CODE : 700026

PHONE : +033 24660329

E-MAIL : communications@databrio.com

WEBSITE : http://www.databrio.com/