Time Series Analysis- Worked Example Part A

Описание: Time Series Analysis- Worked Example Part A

Certainly! Here's a brief synopsis of the tasks outlined:

1. **Simulate a Time Series**: Generate a time series with 500 observations using specified parameters including a seed value of 100, autoregressive parameter (ar) of 0.9, moving average parameter (ma) of 0.2, and order (1,1,1).

2. **General Features of the Chart**: Analyze and comment on the main characteristics observed in the generated time series chart, such as trends, patterns, and any anomalies.

3. **ACF and PACF**: Plot the sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) to study the dependency structure of the time series data over different lags.

4. **Least Squares Linear Fit**: Find the best least squares linear fit for the data, add this trend line to the initial time series chart, and provide the updated chart.

5. **Stationarity and Residuals**: Evaluate if the linear trend from the least squares fit can be removed to achieve stationarity in the residuals, which is crucial for further time series modeling.

6. **Model Fitting**: Fit different models including AR(1), AR(3), and ARMA(1,1) to the time series data to identify the best-fitting model for capturing the underlying structure of the data.

I hope this summary helps! If you need more details on any specific section, feel free to ask.