- Financial Time Series Data
- Exploring Time Series Data in R
- Plotting Time Series in R
- Handling Missing Values in Time Series
- Creating a Time Series Object in R
- Check if an object is a time series object in R
- Plotting Financial Time Series Data (Multiple Columns) in R
- Characteristics of Time Series
- Stationary Process in Time Series
- Transforming a Series to Stationary
- Time Series Transformation in R
- Differencing and Log Transformation
- Autocorrelation in R
- Time Series Models
- ARIMA Modeling
- Simulate White Noise (WN) in R
- Simulate Random Walk (RW) in R
- AutoRegressive (AR) Model in R
- Estimating AutoRegressive (AR) Model in R
- Forecasting with AutoRegressive (AR) Model in R
- Moving Average (MA) Model in R
- Estimating Moving Average (MA) Model in R
- ARIMA Modelling in R
- ARIMA Modelling - Identify Model for a Time Series
- Forecasting with ARIMA Modeling in R - Case Study
- Automatic Identification of Model Using auto.arima() Function in R
- Financial Time Series in R - Course Conclusion

# ARIMA Modeling

If we combine differencing with autoregression and a moving average model, we obtain a non-seasonal ARIMA model. ARIMA is an acronym for **AutoRegressive Integrated Moving Average** model. The term "integration" in this context is the reverse of differencing.

ARIMA model is represented as **ARIMA(p,d,q)**

Where:

- p = order of the autoregressive part
- d = degree of first differencing involved
- q = order of the moving average part

A series which is stationary after being differentiated once is said to be integrated of order 1 and is denoted by I(1). In general a series which is stationary after being differentiated d times is said to be integrated of order d, denoted I(d). A series which is stationary without differencing is said to be I(0).

While using ARIMA modeling for time series forecasting, selecting appropriate values for p, d and q can be difficult. We make use of ACF, PACF and other functions to help us determine these values.

Many of the models we previously discussed can be easily explained by the ARIMA model as shown below:

- White noise: ARIMA(0,0,0)
- Random walk: ARIMA(0,1,0) with no constant
- Random walk with drift: ARIMA(0,1,0) with a constant
- Autoregression: ARIMA(p,0,0)
- Moving average: ARIMA(0,0,q)

### ARIMA Modeling in R

In the next few lessons, we will learn about how we can simulate and estimate these models in R using the ARIMA class of functions.