STAT 474 Project

Load Packages (Code 1)

Assigning variable to dataset. (Code 2)

Transforming the Quarter variable into integer. (Code 3)

Turning the data into a useable time series. (Code 4)

#Introduction:

We will be analzying the “basic-quarterly-iron-production.csv” dataset. The goal is to remove all trend. Plot the acf and pacf, and make sure the residuals are in range. Find a model that suits the data. Then to make a prediction for 1994 Quarter 4. Run a spectral analysis.

#Methods:

Remove the trend with a diff and log. It is not white noise, clear signs in the biggining of 1980 and 1990. Plot the acf to see what model we should pick. (Code 5)

Plotting the acf and pacf. (Code 6)

        ACF  PACF
 [1,] -0.22 -0.22
 [2,] -0.21 -0.27
 [3,] -0.13 -0.27
 [4,]  0.25  0.10
 [5,] -0.03 -0.02
 [6,] -0.03  0.03
 [7,]  0.00  0.07
 [8,]  0.01 -0.01
 [9,] -0.01  0.01
[10,]  0.03  0.04
[11,]  0.03  0.04
[12,] -0.01  0.04
[13,]  0.03  0.08
[14,]  0.04  0.09
[15,] -0.15 -0.13
[16,]  0.09  0.06
[17,]  0.01 -0.03
[18,] -0.05 -0.11
[19,]  0.01  0.06
[20,]  0.13  0.11
[21,]  0.02  0.11
[22,] -0.16 -0.04
[23,] -0.02 -0.06

After running the log and diff to smooth the series, we see that a arima model is needed as there are clear signs on non stationarity. (Code 7)

The rediduals do not exceed the blue lines (significance). This suggest the model fits the series well.

Now it is time to forecast for 1994 quarter 4. Results show. (Code 8)

$pred
            Qtr4
1994 -0.07415435

$se
           Qtr4
1994 0.08289713

After running the spectral, we see that the dominant frequency are at every 5th quarter and every 3 quarters. (Code 9)

#Results

From our methods, of taking the diff and log of the series which removed the trend aspect. After remvoing the trend, we plotted the acf and pacf and saw signs of nonstationary. We then started looking for a model which we found that arima(1,0,1) seasonal(1,1,1) fit well. Now, moving onto forecasting we found 1994 Quarter 4, which looks like a drop in the series.

#Conclusion

In conclusion, we found a model that fit the series well, and we were able to successful forecast the missing quarter of 1994.

#AppendixCode (Code 1) require(astsa) require(tidyverse) library(stringr)

(Code 2) iron=read.csv(“basic-quarterly-iron-production.csv”)

iron

(Code 3) iron<- iron %>% mutate(Quarter=ts(Quarter, start = 1956, end = 1994.75, frequency = 4)) iron

(Code 4) iron_ts1 <- ts(iron$Basic.quarterly.iron.production.in.Australia..thousand.tonnes..Mar.1956…Sep.1994, start = 1956, end = 1994.5, frequency = 4) tsplot(iron_ts1)

(Code 5) tsplot(diff(log(iron_ts1))) IronTsDiffLog<-diff(log(iron_ts1))

(Code 6) acf2(IronTsDiffLog)

(Code 7) abc <- arima(IronTsDiffLog, order=c(1,0,1), seasonal= list(order=c(1,1,1))) acf(abc$residuals)

(Code 8) sarima.for(IronTsDiffLog, n.ahead=1,1,0,1,1,1,1,12)

(Code 9) mvspec(IronTsDiffLog)