MATH 5045 Assignment 1 Gerald Cheang School of ITMS University of South Australia This assignment is due on Wed 16th Sept 23.55 hrs, to be submitted online as a single pdf file or in another suitable...

instructions are clear in the file. i dont know the no of words for the report but process and steps has to be clearly explained. its time series model in R. give me assurance whether you can do it or not


MATH 5045 Assignment 1 Gerald Cheang School of ITMS University of South Australia This assignment is due on Wed 16th Sept 23.55 hrs, to be submitted online as a single pdf file or in another suitable format as a single file. A link in the course website will be opened closer to the due date of the assignment. You may discuss the assignment with one another but the final write up must be your own work. All data can be found in the data library in R . 1. Use the Nile data set from and including the readings for 1899 onwards. (a) Plot its correlogram and partial correlogram. (b) Fit a suitable autoregressive model to the data. (c) Write down an equation for the model using the parameter estimates. (d) Suppose we are now living in 1970. Use your fitted model to predict the flow rate for 1971 to 1980. Comment on your results. 2. Consider the New Haven yearly temperature data. (a) Plot its correlogram and partial correlogram. (b) Fit a suitable autoregressive model to the data. (c) Suppose we are now living in 1971. Use your fitted model to predict the average yearly temperature for 1972 to 1976. Comment on your results. (d) From about 1927 onwards, the mean of average yearly temperatures looks like it has shifted up by a little bit. Repeat parts (a), (b) and (c) for the data from 1927 onwards. 1 3. Look at the Lake Huron data set. (a) Taking the entire data, plot its correlogram and partial correlogram. (b) Fit a suitable autoregressive model to the data. (c) Now if you look at the plot of the data, it looks like there might be a change in the average flow from about 1890 onwards. This might be due to the beginning of dredging operations of parts of Lake Huron, its inlets and outlets, and in other lakes linked to it. Now look at the flow from 1890 onwards and repeat parts (a) and (b). (d) Which might be a better model? Take the data as a whole or take the data from 1890 onwards? Note that using the arima( ) command instead of the ar( ) command for both cases would give you a criterion that allows you to decide. (e) Using the model that is more suitable, predict the flow rate for 1973 to 1980, assume that we are now in 1972. 2