Time series Series with Power BI- Arima Model-Part 11

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aqd

In the last post, I have explained the d value for model ARIMA (p,d,q).

In this post, I am going to show how to identify the p and q values as below.

one of the main difference between exponential smoothing and Arima is that Arima considers the correlation of a value at a time with other values which we call autocorrelation.

to see this autocorrelation we need two charts:acf and pacf. but what they are and how they are related to p and q value

acf value or q

acf or (Autocorrelation chart). tries to find a correlation between a value and it successive. there may be a correlation between the value in time t and time t-1. however, these the value in time t may be also related to time 1,2 or any other time.

acf

 

I create a plot for acf and for kings death age.

what we have is below chart, this chart shows how the value in a different time from 1 to 20 is correlated to current time values. for instance for current time the correlation is 1 with itself. in time 2 it is a bit high and we can say there is a correlation between values in time 1 and time 2., however, we could not see any other correlation after time 2.  so the value for q will be 1 as, after time one, we have no correlation.

pcf-kings

pacf Value or p

now, we are going to see what is pacf value. pacf is partial autocorrelation values, that means we just purely consider the autocorrelation between time t and time t-1 with removing other correlation with t1,t2 or any other time, we just consider the correlation between time 1 and time 2.

pacf

now, we are going to see this partial correlation

 

apcf-kings

above picture shows there is a correlation between time 1 and time 2 and 3 after time 3 there is no correlation. so p=3.

in other words we able to model our ARIMA model as

ARIMA(p=3,d=1,q=1) however, we able to choose we also below models

ARIMA(p=3,d=1,q=0)

ARIMA(p=0,d=1,q=1)

there is a rule that we better to choose a model with lower value so the final ARIMA model would be :ARIMA(0,1,1)

The above times series does not have any seasonality. in the next post, I will show you how to create an ARIMA model that support seasonality. Then I will explain how to forecast data.

http://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/src/timeseries.html

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Leila Etaati
Dr. Leila Etaati is Principal Data Scientist, BI Consultant, and Speaker. She has over 10 years’ experience working with databases and software systems. She was involved in many large-scale projects for big sized companies. Leila has PhD of Information System department, University of Auckland, MS and BS in computer science. Leila is Microsoft Data Platform MVP.

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