Time Series Analysis

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DATA BRIO ACADEMY DATA BRIO ACADEMY

TIME SERIES

ANALYSIS

What is a Time Series? What is a Time Series?

Databrio

2/18/2016

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When we have a

When we have a chronologicchronologically ordered collection (set) of ally ordered collection (set) of data points, wedata points, we

refer to the data set as time

refer to the data set as time series. So, a time series is a series. So, a time series is a sequence ofsequence of

observations taken sequentially in time series

observations taken sequentially in time series data can have both univariatedata can have both univariate

and multivariate quantitative data collected over time.

For example, let us say that we have the

For example, let us say that we have the attrition rate data of a company forattrition rate data of a company for

the past 12

the past 12 months. The senior manager wants to know the months. The senior manager wants to know the probable attritionprobable attrition

rate for the 13

rate for the 13thth and 14 and 14thth month, so that he can prepare his current month, so that he can prepare his current

workforce and initiate any recruitment process if necessary. As we

workforce and initiate any recruitment process if necessary. As we have thehave the

data points arranged chronologically, we say that the data

data points arranged chronologically, we say that the data is ais a time seriestime series data

data.. For predicting the For predicting the probable attrition rate for any future period, weprobable attrition rate for any future period, we

have to use time series analysis which has been discussed belo

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There are two classes of

There are two classes of time series process: Stationary and Non-Stationarytime series process: Stationary and Non-Stationary

So, what is stationarity? Covariance stationarity follows three

conditions-1) Unconditional mean and variance should be constant

1) Unconditional mean and variance should be constant

E(Y

E(Ytt) = E(Y) = E(Yt+jt+j) = µ) = µ

Var (Y

Var (Ytt) = Var(Y) = Var(Yt+jt+j)=σ )=σ 22

2) Covariance depends on time

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

reference period.

Cov(Y

Cov(Ytt,Y,Yt+jt+j) = Cov(Y) = Cov(Yss,Y,Ys+js+j) = γ) = γ

Any

Any time series datatime series data which follows the which follows the above mentioned conditions are knownabove mentioned conditions are known

as stationary time series. Similarly, if a time series data do

as stationary time series. Similarly, if a time series data do not conform tonot conform to

the above conditions, they are termed as

the above conditions, they are termed as non-stationary time series data. Fornon-stationary time series data. For

a non-stationary time series, the mean, variance and

a non-stationary time series, the mean, variance and the covariance changes.the covariance changes.

There is no long-run mean to which the series returns. Also, the variance is

tie-dependent

tie-dependent, for eg., it , for eg., it could go to infinity as the number could go to infinity as the number of observationof observation

goes to infinity.

Unit root tests are used to find

Unit root tests are used to find out non-stationary time series. One of theout non-stationary time series. One of the

commonly used tests for

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

At first, using unit root

At first, using unit root tests find out whether the time series is stationarytests find out whether the time series is stationary

or not. If it is

or not. If it is stationary, procestationary, proceed to find out ed to find out the best ARMA model usingthe best ARMA model using

different diagnostic tests. After selecting the best

different diagnostic tests. After selecting the best suited model, forecast forsuited model, forecast for

future periods and again use different diagnostic tests to find out

future periods and again use different diagnostic tests to find out how goodhow good

the forecast is.

If in case the unit

If in case the unit root test like “Dickeyroot test like “Dickey--Fuller” test shows the time series toFuller” test shows the time series to

be non-stationary, then you have to transform the

be non-stationary, then you have to transform the data into stationary series.data into stationary series.

Differencing is widely used to transform the data into stationary series.

Once, the data is

Once, the data is transformed into stationary time series, follow the previoustransformed 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

After identification of a stationary time series process, estimation and modelprocess, estimation and model

selection is done. Stationary Process can be of three basic types:

1.

1. Autoregressive(AR)-Autoregressive(AR)-It means that the It means that the variable is a function of variable is a function of its ownits own

lagged values upto a maximum lag of

lagged values upto a maximum lag of p.p.

2.

2. Moving Average(MA)-It means the variable is a function of Moving Average(MA)-It means the variable is a function of thethe

disturbances upto a maximum lag of q.

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3. Combined(ARMACombined(ARMA)-It includes both the elements, i.e. )-It includes both the elements, i.e. have lagged values have lagged values ofof

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

series is a pure AR/ MA or ARMA process. Then estimate the specificationsor ARMA process. Then estimate the specifications

like auto-covariance, auto-correlation and partial

like auto-covariance, auto-correlation and partial auto- correlation.auto- correlation.

Finally,

Finally, choose the best model choose the best model based on based on the significance of coefficients, whitethe significance of coefficients, white

noise residuals, fit vs parsimony and ability to forecast.

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