What is pacf in arima in R

This recipe explains what is pacf in arima in R

Recipe Objective

What is pacf in arima in R?

Time series is a statistical technique that deals with time series data or trend analysis. Time series data means the data is collected over a period of time/ intervals. Time series data helps us with making forecasting based on the previously collected data. ARIMA is a time series forecasting method where AR stands for Autoregressive and MA stands for Moving Average. The AR model is based on the assumption that the data collected is stationary and univariate, and the forecast corresponds to a linear combination of previous data of the variables. The pacf () function is used for finding the partial auto correlation between the series and lags. Which means the partial correlation states the correlation between all the time series data points are exactly 'k' steps apart. The pacf () function thus is useful to identify the number of auto regressions (AR) coefficient present in an ARIMA time series model. This recipe demonstrates an example of pacf in arima in time series.

Learn Time Series Forecasting using ARIMA Model in Python

Step 1 - Install required package

install.packages('forecast')
library(forecast)

Step 2 - Generate random time series data

# Get the data points in form of a R vector.
rain <- c(987,1025,978,774,1563,569,1456,789,1479,566,1563,1698)
# Convert it to a time series object.
rain_ts <- ts(rain,start = c(2020,1),frequency = 12)
# Print the timeseries data.
print(rain_ts)
plot(rain_ts, main = "Time series data")
summary(rain_ts)

Step 3 - Plot a trend line

plot(rain_ts)
abline(reg=lm(rain_ts~time(rain_ts)))

Step 4 - Build a model using arima()

model <- arima(rain_ts, order = c(1,0,0))
model
model <- arima(rain_ts, order = c(2,0,0))
model

We can try to fit different 'ar models' by changing the order/ The lower the aic term , the better the model. Hence we choose the a model with order - (1,0,0)

Step 5 - Plot a pacf()

pacf(ts(diff(log10(rain_ts))),main='PACF for rain_ts')

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