ARIMA Model for Time Series Analysis

Architecture of ARIMA model

Before implementing the ARIMA model, we must note the three components of the model- p, q & d.

We identify the ARIMA model by three terms:

p- refers to the order of the AR term

q- refers to the order of the MA term

d- refers to the number of differencing to make time series stationary.

Implementing analysis with ARIMA Model

Let's now build the ARIMA model for time series analysis. We will be going through several steps to achieve the same.

Implementing ARIMA in R

First, we read the dataset. Note that in this blog, we will be using the dataset - ‘WWWusage.txt’ available online.

usage=scan('C:/Users/komal/Desktop/wwwusage.txt', skip=1)

Then, we plot the dataset.

plot(1:100, usage, xlim = c(0, 100), ylim=c(80, 250))

To connect the points,

lines(1:100, df, type="l")

Interpretation of sample ACF and PACF plot

Autocorrelation coefficient function(ACF) refers to how the data points are related to the preceding data points.points.

Partial autocorrelation coefficient function(PACF) specifies  specifies  the dependence structure of a stationary process.

acf(usage, lag.max=100)

pacf(usage, lag.max=100)

We conclude that the data is not stationary.

Now, we take first order differencing,

z = diff(usage, 1, 1)
plot(1:99, z, xlim = c(0, 100), ylim=c(-15, 15))
lines(1:99, z, type="l" )

acf(z, lag.max=100)
pacf(z, lag.max=100)

Take second order differencing,

z = diff(usage, 1, 2)
plot(1:98, z, xlim = c(0, 120), ylim=c(-15, 15))
lines(1:98, z, type="l" )

acf(z, lag.max=100)
pacf(z, lag.max=100)

Now, the ACF decay very fast, so the data is stationary

Now, before going further, we should know what AIC is. AIC is the Akaike Information Criteria. It is a widely used measure of a statistical model. It helps in quantifying the goodness of a statistical fit and the simplicity of a model in a single statistic.

Model-1 ARIMA

ft = arima(usage, order = c(0,2,2))
tsdiag(ft)                             

The AIC criterion value for Model 1 ARIMA(0,2,2) = 517.211

Model-2 ARIMA

ft2 = arima(usage, order = c(2,2,0))
tsdiag(ft2)

The AIC criterion value for Model 2 ARIMA(2,2,0) = 511.46

Model-3 ARIMA

library(forecast)
ft3 = auto.arima(usage)
tsdiag(ft3)

The AIC value for model 3 ARIMA(1,1,1) = 514.55

 It's known that lower the AIC criterion value, the better the model. Observing the AIC values of the models, we choose the Model 2 ARIMA (2,2,0) as the final fitted model  for wwwusage data as it gives the lowest AIC (511.46). 

Frequently Asked Questions

What is the difference between time series analysis and time series forecasting?

In time series analysis, we understand and analyze the dataset. In forecasting, we predict based on the analysis already made.

Is it important for a Time Series to be Stationary in the ARIMA model?

Yes, Stationarity is very important because a model describing the data might vary in accuracy at different time points in its absence.

What is SARIMA?

SARIMA refers to Seasonal-ARIMA and the name is justified as it includes seasonality contribution. The importance of seasonality is evident.

Conclusion

We hope this blog helped you understand the fundamental concepts of Time Series Analysis along with the ARIMA model and it's implementation

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