Discussion Posts
Priyanka Gagneja
March 27, 2018
Discussion #3
Go to Data Market (https://datamarket.com/data/list/?q=cat:ecc%20provider:tsdl (Links to an external site.) Pick a time series of interest to you. Using this data (be sure to sort in ascending order), build two or three ETS models. Which performs better? What explanation might explain that?
I continue with - Weekly closings of the Dow-Jones industrial average, July 1971 – August 1974.
# Loading libraries
library(forecast)
library(xts)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(TTR)
library(tseries)
library(ggplot2)
# LOADING DATASET
# weekly-closings-of-the-dowjones.csv
dj<-read.csv(file.choose())
names(dj)## [1] "Week" "close.price"names(dj)[2]<-c("close.price")
head(dj)## Week close.price
## 1 1971-W27 890.19
## 2 1971-W28 901.80
## 3 1971-W29 888.51
## 4 1971-W30 887.78
## 5 1971-W31 858.43
## 6 1971-W32 850.61Plotting data
# Plot original series
plot(dj$close.price,type="l",xlab="Week",ylab="closing price",main="historical data")
# boxplots by month//Qtr
dj.ts.q<-ts(dj,frequency = 4)
dj.ts.m<-ts(dj,frequency = 12)
# boxplot(dj.ts.m[[1]],dj.ts.m["close.price"])Given the weekly data, I am still trying to find out how to make a monthly/quarterly boxplot as discussed in class tonight. However, I tried to gt the weekly boxplots out this time.
dj$weeknum<-substr(dj$Week,6,8)
ggplot(dj, aes(as.factor(dj$weeknum), dj$close.price)) +
geom_boxplot()
And as expected, the weekly data as well is very variable over diff weeks over years.
Forecasting data
dj.ts.m<-ts(dj$close.price,frequency = 12)
# Simple Exponential Smoothing
ses1 <- ses(dj.ts.m, alpha=0.2, initial="simple", h=3)
ses2 <- ses(dj.ts.m, alpha=0.6, initial="simple", h=3)
ses3 <- ses(dj.ts.m, h=3)
# Holt Winters Linear Trend
holt1 <- holt(dj.ts.m, alpha=0.8, beta=0.2, initial="simple", h=5)
# Exponential Trend
holt2 <- holt(dj.ts.m, alpha=0.8, beta=0.2, initial="simple", exponential=TRUE, h=5)
# Damped Trend
# holt3 <- holt(dj.ts.m, alpha=0.8, beta=0.2, damped=TRUE, initial="simple", h=5)
# Results for first model:
holt1$model$state## l b
## Dec 0 890.1900 11.6100000
## Jan 1 892.5120 9.7524000
## Feb 1 901.8929 9.6780960
## Mar 1 893.1222 5.9883398
## Apr 1 890.0461 4.1754542
## May 1 865.5883 -1.5511956
## Jun 1 853.2954 -3.6995342
## Jul 1 854.7352 -2.6716765
## Aug 1 875.1407 1.9437633
## Sep 1 901.9369 6.9142491
## Oct 1 911.9702 7.5380664
## Nov 1 912.7017 6.1767393
## Dec 1 910.3517 4.4713955
## Jan 2 894.4126 0.3893035
## Feb 2 894.1444 0.2577965
## Mar 2 894.0084 0.1790477
## Apr 2 878.7175 -2.9149497
## May 2 857.0565 -6.6641572
## Jun 2 841.2785 -8.4869336
## Jul 2 838.8703 -7.2711795
## Aug 2 816.6718 -10.2566399
## Sep 2 809.8190 -9.5758696
## Oct 2 813.2886 -6.9667764
## Nov 2 848.9364 1.5561264
## Dec 2 855.4985 2.5573268
## Jan 3 870.6512 5.0763946
## Feb 3 880.0815 5.9471850
## Mar 3 889.3657 6.6145935
## Apr 3 907.4921 8.9169402
## May 3 908.6258 7.3602991
## Jun 3 909.1492 5.9929231
## Jul 3 908.1324 4.5909801
## Aug 3 907.8887 3.6240347
## Sep 3 916.3745 4.5964001
## Oct 3 918.2102 4.0442492
## Nov 3 922.6829 4.1299391
## Dec 3 939.3066 6.6286868
## Jan 4 941.0831 5.6582465
## Feb 4 943.6523 5.0404390
## Mar 4 943.5625 4.0144072
## Apr 4 942.0754 2.9140957
## May 4 959.0779 5.7317781
## Jun 4 967.1379 6.1974301
## Jul 4 965.7071 4.6717717
## Aug 4 957.4118 2.0783565
## Sep 4 944.8820 -0.8432636
## Oct 4 942.2718 -1.1966654
## Nov 4 957.4470 2.0777207
## Dec 4 968.9049 3.9537626
## Jan 5 963.6837 2.1187690
## Feb 5 940.7205 -2.8976328
## Mar 5 943.6126 -1.7396919
## Apr 5 944.1266 -1.2889530
## May 5 931.7915 -3.4981728
## Jun 5 936.1067 -1.9355091
## Jul 5 924.6422 -3.8412949
## Aug 5 920.5202 -3.8974449
## Sep 5 924.6845 -2.2850837
## Oct 5 945.8879 2.4126019
## Nov 5 961.0041 4.9533228
## Dec 5 965.8555 4.9329353
## Jan 6 961.6457 3.1043881
## Feb 6 968.9900 3.9523766
## Mar 6 963.5805 2.0799940
## Apr 6 950.9161 -0.8688815
## May 6 944.4334 -1.9916356
## Jun 6 951.1044 -0.2591247
## Jul 6 946.4570 -1.1367626
## Aug 6 933.4321 -3.5144081
## Sep 6 940.2315 -1.4516319
## Oct 6 944.8920 -0.2292156
## Nov 6 976.2286 6.0839422
## Dec 6 992.6705 8.1555430
## Jan 7 1004.6212 8.9145763
## Feb 7 1022.8752 10.7824507
## Mar 7 1025.4755 9.1460335
## Apr 7 1033.4763 8.9169847
## May 7 1030.2707 6.4924574
## Jun 7 1010.7206 1.2839587
## Jul 7 1018.4169 2.5664256
## Aug 7 1042.1887 6.8074909
## Sep 7 1041.2872 5.2657054
## Oct 7 1030.2626 2.0076354
## Nov 7 1009.2860 -2.5892002
## Dec 7 985.9874 -6.7310953
## Jan 8 979.4193 -6.6984991
## Feb 8 977.9282 -5.6570200
## Mar 8 962.3662 -7.6380010
## Apr 8 960.0016 -6.5833170
## May 8 968.4677 -3.5734495
## Jun 8 963.4188 -3.8685241
## Jul 8 930.0781 -9.7629751
## Aug 8 944.8710 -4.8517893
## Sep 8 932.8598 -6.2836659
## Oct 8 952.8032 -1.0382546
## Nov 8 960.9130 0.7913483
## Dec 8 930.0929 -5.5309468
## Jan 9 948.0084 -0.8416543
## Feb 9 931.7453 -3.9259311
## Mar 9 901.6999 -9.1498375
## Apr 9 923.1820 -3.0234448
## May 9 899.1997 -7.2152151
## Jun 9 914.3969 -2.7327347
## Jul 9 893.1728 -6.4310011
## Aug 9 881.2044 -7.5384942
## Sep 9 888.1012 -4.6514337
## Oct 9 872.7779 -6.7857923
## Nov 9 881.9904 -3.5861372
## Dec 9 904.4009 1.6131758
## Jan 10 930.5708 6.5245302
## Feb 10 914.5151 2.0084763
## Mar 10 865.2087 -8.2544907
## Apr 10 868.8628 -5.8727656
## May 10 863.3900 -5.7927781
## Jun 10 881.5754 -0.9971361
## Jul 10 895.0197 1.8911341
## Aug 10 888.4702 0.2030067
## Sep 10 920.0546 6.4793001
## Oct 10 942.9868 9.7698708
## Nov 10 967.5513 12.7288056
## Dec 10 978.9600 12.4647837
## Jan 11 969.2690 8.0336139
## Feb 11 985.1085 9.5948017
## Mar 11 947.1647 0.0870710
## Apr 11 916.1863 -6.1260065
## May 11 895.0761 -9.1228610
## Jun 11 860.3906 -14.2353741
## Jul 11 827.0311 -18.0602169
## Aug 11 832.2342 -13.4075507
## Sep 11 816.2853 -13.9158094
## Oct 11 815.4579 -11.2981316
## Nov 11 839.2480 -4.2804950
## Dec 11 871.1775 2.9615115
## Jan 12 848.0118 -2.2639290
## Feb 12 853.5256 -0.7083885
## Mar 12 858.0754 0.3432618
## Apr 12 846.8357 -1.9733300
## May 12 825.2925 -5.8873156
## Jun 12 820.1370 -5.7409422
## Jul 12 847.6712 0.9140832
## Aug 12 851.2531 1.4476350
## Sep 12 872.9801 5.5035237
## Oct 12 885.9607 6.9989377
## Nov 12 881.0959 4.6261905
## Dec 12 854.4884 -1.6205495
## Jan 13 848.6056 -2.4730095
## Feb 13 845.0745 -2.6846200
## Mar 13 856.3980 0.1169971
## Apr 13 839.0150 -3.3829990
## May 13 843.8464 -1.7401184
## Jun 13 848.7733 -0.4067233
## Jul 13 824.7453 -5.1309686
## Aug 13 817.2429 -5.6052627
## Sep 13 804.0635 -7.1200795
## Oct 13 842.3647 1.9641699
## Nov 13 843.3378 1.7659526
## Dec 13 821.3327 -2.9882433
## Jan 14 805.5969 -5.5377635
## Feb 14 793.4278 -6.8640254
## Mar 14 787.0968 -6.7574337
## Apr 14 786.4199 -5.5413260
## May 14 783.8317 -4.9506923
## Jun 14 757.8402 -9.1588548fitted(holt1)## Jan Feb Mar Apr May Jun Jul
## 1 901.8000 902.2644 911.5710 899.1105 894.2216 864.0371 849.5959
## 2 914.8231 894.8019 894.4022 894.1875 875.8025 850.3924 832.7915
## 3 858.0558 875.7276 886.0287 895.9803 916.4090 915.9861 915.1421
## 4 945.9353 946.7413 948.6927 947.5769 944.9895 964.8097 973.3354
## 5 972.8587 965.8025 937.8229 941.8729 942.8376 928.2934 934.1712
## 6 970.7884 964.7501 972.9424 965.6605 950.0472 942.4418 950.8452
## 7 1000.8260 1013.5358 1033.6576 1034.6216 1042.3933 1036.7631 1012.0046
## 8 979.2563 972.7208 972.2711 954.7282 953.4183 964.8942 959.5503
## 9 924.5619 947.1667 927.8194 892.5500 920.1586 891.9845 911.6642
## 10 906.0140 937.0953 916.5235 856.9542 862.9901 857.5972 880.5783
## 11 991.4248 977.3026 994.7033 947.2517 910.0603 885.9532 846.1553
## 12 874.1390 845.7479 852.8172 858.4187 844.8624 819.4052 814.3961
## 13 852.8679 846.1326 842.3899 856.5150 835.6320 842.1063 848.3665
## 14 818.3445 800.0591 786.5638 780.3393 780.8785 778.8810
## Aug Sep Oct Nov Dec
## 1 852.0635 877.0845 908.8511 919.5083 918.8784
## 2 831.5991 806.4152 800.2432 806.3219 850.4925
## 3 912.7234 911.5127 920.9709 922.2544 926.8128
## 4 970.3788 959.4901 944.0388 941.0751 959.5247
## 5 920.8009 916.6227 922.3995 948.3005 965.9574
## 6 945.3203 929.9176 938.7799 944.6628 982.3125
## 7 1020.9833 1048.9962 1046.5529 1032.2702 1006.6968
## 8 920.3151 940.0192 926.5762 951.7650 961.7043
## 9 886.7418 873.6659 883.4497 865.9922 878.4043
## 10 896.9108 888.6732 926.5339 952.7567 980.2801
## 11 808.9708 818.8266 802.3695 804.1598 834.9675
## 12 848.5853 852.7007 878.4837 892.9597 885.7221
## 13 819.6143 811.6376 796.9434 844.3289 845.1037
## 14holt1$mean## Jul Aug Sep Oct Nov
## 14 748.6813 739.5225 730.3636 721.2048 712.0459Plotting forecasts
# Simple Exponential Smoothing
plot(ses1, ylab="Dow Jones Closing Price", xlab="Year", main="", fcol="white", type="o")
lines(fitted(ses1), col="blue", type="o")
lines(fitted(ses2), col="red", type="o")
lines(fitted(ses3), col="green", type="o")
lines(ses1$mean, col="blue", type="o")
lines(ses2$mean, col="red", type="o")
lines(ses3$mean, col="green", type="o")
legend("topleft",lty=1, col=c(1,"blue","red","green"), c("data", expression(alpha == 0.2), expression(alpha == 0.6), expression(alpha == 0.89)),pch=1)
# Holt Winter Method with Linear/ Exp/ Damped Trend.
plot(holt2, type="o", ylab="Dow Jones Closing Price ", xlab="Year", fcol="white", plot.conf=FALSE)## Warning in plot.window(xlim, ylim, log, ...): "plot.conf" is not a
## graphical parameter## Warning in title(main = main, xlab = xlab, ylab = ylab, ...): "plot.conf"
## is not a graphical parameter## Warning in axis(1, ...): "plot.conf" is not a graphical parameter## Warning in axis(2, ...): "plot.conf" is not a graphical parameter## Warning in box(...): "plot.conf" is not a graphical parameterlines(fitted(holt1), col="blue")
lines(fitted(holt2), col="red")
# lines(fitted(holt3), col="green")
lines(holt1$mean, col="blue", type="o")
lines(holt2$mean, col="red", type="o")
# lines(holt3$mean, col="green", type="o")
legend("topleft", lty=1, col=c("black","blue","red"), # ,"green"
c("Data","Holt's linear trend","Exponential trend")) # ,"Additive damped trend"
Which ones better ?
ses3.me<-mean(na.omit(ses3$residuals))
ses3.mae<-mean(na.omit(abs(ses3$residuals)))
ses3.mse<-mean(na.omit(ses3$residuals)^2)
ses3.rmse<-sqrt(ses3.mse)
ses3.mape<-mean(abs(na.omit(ses3$residuals/ses3$x)))
holt1.me<-mean(na.omit(holt1$residuals))
holt1.mae<-mean(na.omit(abs(holt1$residuals)))
holt1.mse<-mean(na.omit(holt1$residuals)^2)
holt1.rmse<-sqrt(holt1.mse)
holt1.mape<-mean(abs(na.omit(holt1$residuals/holt1$x)))
r<-c("Mean Error","Mean Absolute Error", "Mean Squared Error", "Root Mean Sq Error", "Mean Absolute Percentage Error")
m<-c(ses3.me,ses3.mae,ses3.mse,ses3.rmse,ses3.mape)
a<-c(holt1.me,holt1.mae,holt1.mse,holt1.rmse,holt1.mape)
bv<-c("Bias","Variance","Variance","Bias","Variance")
result<- data.frame(cbind(m,a,bv))
row.names(result)<-r
result## m a
## Mean Error -0.878700375040265 -0.801267545602839
## Mean Absolute Error 15.4264590754452 16.5954338314235
## Mean Squared Error 389.39943276017 444.779962363359
## Root Mean Sq Error 19.7332063476813 21.0898070726918
## Mean Absolute Percentage Error 0.0171491707785437 0.0184287544298628
## bv
## Mean Error Bias
## Mean Absolute Error Variance
## Mean Squared Error Variance
## Root Mean Sq Error Bias
## Mean Absolute Percentage Error VarianceResults/Conclusions
Looking at the residual plots in this case I believe the Holts’ Linear Trend model (in blue) fits in the best. However, with respect to the error term both seem at par for Holts’ Linear Trend and Simple exponential with high alpha high value(0.9).