- 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
Time Series Models
By now we have a strong foundational understanding of various concepts essential for time series analysis. The rest of the course will focus on the following:
- A theoretical understanding of the important time series models (White Noise, AutoRegressive (AR), Moving Average (MA), ARMA.
- The ARIMA model and how various time series processes can be explained by ARIMA.
- Simulating and estimating these time series models in R.
- Box-Jenkins (B-J) methodology for time series forecasting.
- A comprehensive case study for time series analysis in R (With code and plots).
Time Series Models
The objective of the following text is to provide a theoretical understanding of the time series models. It can be a bit complex to grasp, however, as we move to practical implementation in the next lessons, things will start to make more sense.
White Noise is the simplest example of a stationary process and is also the foundation of the other models we will discuss. A white noise process is a random process of random variables that are uncorrelated, have mean zero, and a finite variance. In other words, a series is called white noise if it is purely random in nature. Random noise is donated by εt
Plots of white noise series exhibit a very erratic, jumpy, unpredictable behavior. Since the εt are uncorrelated, previous values do not help us to forecast future values. White noise series themselves are quite uninteresting from a forecasting standpoint (they are not linearly forecastable), but they form the building blocks for more general models.
Simple Time Series Models
A simple trend model can be expressed as follows:
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