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Copy and paste the following data into an Excel (.csv) file:

```
DATE,HOUSTNSA
1/1/1991,52.5
2/1/1991,59.1
3/1/1991,73.8
4/1/1991,99.7
5/1/1991,97.7
6/1/1991,103.4
7/1/1991,103.5
8/1/1991,94.7
9/1/1991,86.6
10/1/1991,101.8
```

Then, do the following in R:

(i) Plot the time series HOUSTNSA.

(ii) Estimate both trend and seasonality for the data from 1999:01 to 2021:12. Try different models and choose the best models. Report the best estimated equations for trend and seasonality. Explain why you chose the model.

(iii) Forecast the point values and construct the interval forecasts for 2022:01 to 2022:12 based on the estimations in (ii), and plot the graph against true values for 2022:01 to 2022:12.

Answer :

Final answer:

To plot the time series HOUSTNSA in R, import the data from the CSV file, convert the 'DATE' column to a date format, and use the 'plot' function. To estimate trend and seasonality, try different models and choose the best model based on criteria like AIC or BIC. Forecast the point values and construct interval forecasts for 2022:01-2022:12 using the chosen model. Plot the forecasted values against the true values using the 'autoplot' function.

Explanation:

To plot the time series HOUSTNSA in R, you can follow these steps:

  1. First, import the data from the CSV file into R using the 'read.csv' function.
  2. Next, convert the 'DATE' column to a date format using the 'as.Date' function.
  3. Plot the time series using the 'plot' function, specifying the 'DATE' column as the x-axis and the 'HOUSTNSA' column as the y-axis.

To estimate trend and seasonality for the data from 1999:01-2021:12, you can try different models such as additive or multiplicative models. For each model, you can use the 'decompose' function to decompose the time series into trend, seasonal, and residual components. The best model can be chosen based on criteria like the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC).

Once you have chosen the best model, you can use the 'forecast' function to forecast the point values and construct interval forecasts for 2022:01-2022:12. The forecasted values can be plotted against the true values using the 'autoplot' function from the 'ggplot2' package.

Learn more about time series analysis and forecasting in r here:

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