Load Data
setwd("~/Documents/MSAE/Predictive Analytics")
AAPLdata <- read.csv("AAPL (1).csv")
MSFTdata <- read.csv("MSFT.csv")
AMBCdata <- read.csv("AMBC.csv")
BACdata <- read.csv("BAC.csv")
Data Manipulation
#change variable names for monthly adj. close
AAPLdata <- rename(AAPLdata, AAPL = Adj.Close)
AMBCdata <- rename(AMBCdata, AMBC = Adj.Close)
BACdata <- rename(BACdata, BAC = Adj.Close)
MSFTdata <- rename(MSFTdata, MSFT = Adj.Close)
#combine datasets
AAPLdata <- AAPLdata[c(1,6)]
AMBCdata <- AMBCdata[c(1,6)]
BACdata <- BACdata [c(1,6)]
MSFTdata <- MSFTdata[c(1,6)]
stockdata <- merge(AAPLdata, AMBCdata, by = "Date")
stockdata <- merge(stockdata, BACdata, by = "Date")
stockdata <- merge(stockdata, MSFTdata, by = "Date")
stockdata$Date <- as.Date(stockdata$Date)
stockdata <- rename(stockdata, Month = Date)
#Creating Tsibble
stockdata <- stockdata %>%
mutate(Month = yearmonth(Month)) %>%
tsibble(index = Month)
Building Training and Test Set
training <- stockdata[1:48,]
test <- stockdata[49:60,]
#Pivot Longer
temp <- stockdata %>%
pivot_longer(!c(Month), names_to='Stock', values_to='Value')
training <- training %>%
pivot_longer(!c(Month), names_to='Stock', values_to='Value')
test <- test %>%
pivot_longer(!c(Month), names_to='Stock', values_to='Value')
#Assign Sector
temp$Sector = rep('Tech', nrow(temp))
training$Sector = rep('Tech', nrow(training))
test$Sector = rep('Tech', nrow(test))
temp$Sector[temp$Stock=="AMBC"|temp$Stock=="BAC"]="Finance"
training$Sector[training$Stock=="AMBC"|training$Stock=="BAC"]="Finance"
test$Sector[test$Stock=="AMBC"|test$Stock=="BAC"]="Finance"
temp %>% autoplot()
## Plot variable not specified, automatically selected `.vars = Value`
Different aggregate groups
myagg <- temp %>% aggregate_key(Stock/Sector, Value = sum(Value))
myagg2 <- training %>% aggregate_key(Stock, Value = mean(Value))
myagg3 <- training %>% aggregate_key(Sector/Stock, Value = mean(Value))
agg_test <- test %>% aggregate_key(Sector/Stock, Value = mean(Value))
#aggregate plot
myagg %>%
filter(is_aggregated(Sector)) %>%
autoplot(Value) +
labs(y= "Value", title = "Value of Investment") +
facet_wrap(vars(Stock), scales = "free_y", ncol = 3) +
theme(axis.text.x = element_text (angle = 90, hjust = 1)) +
theme(legend.position = "none")
Models
Bottoms up forecast
m1 <- myagg2 %>% model(ets = ETS(Value)) %>% reconcile(bu =bottom_up(ets))
f1 <- m1 %>% forecast(h=12)
f1 %>% autoplot(temp)
acc1 <- f1 %>% accuracy(test %>% aggregate_key(Stock, Value = mean(Value)))
Middle Out forecast
m2 <- myagg3 %>% model(ets2 = ETS(Value)) %>% reconcile(md =middle_out(ets2))
f2 <- m2 %>% forecast(h=12)
f2 %>% autoplot(temp %>% aggregate_key(Sector/Stock, Value = mean(Value))) +
facet_wrap(~Stock + Sector) +
theme(axis.text.x = element_text (angle = 90, hjust = 1))
acc2 <- f2 %>% accuracy(test %>% aggregate_key(Sector/Stock, Value = mean(Value)))
Top Down forecast
m3 <- myagg3 %>% model(ets3 = ETS(Value)) %>% reconcile(td = top_down(ets3))
f3 <- m3 %>% forecast(h=12)
f3 %>% autoplot(temp %>% aggregate_key(Sector/Stock, Value = mean(Value))) +
facet_wrap(~Stock + Sector) +
theme(axis.text.x = element_text (angle = 90, hjust = 1))
acc3 <- f3 %>% accuracy(test %>% aggregate_key(Sector/Stock, Value = mean(Value)))
MinT Forecast
m4 <- myagg3 %>% model(ets4 = ETS(Value)) %>% reconcile(mint = min_trace(ets4))
f4 <- m4 %>% forecast(h=12)
f4 %>% autoplot(temp %>% aggregate_key(Sector/Stock, Value = mean(Value))) +
facet_wrap(~Stock + Sector) +
theme(axis.text.x = element_text (angle = 90, hjust = 1))
acc4 <- f4 %>% accuracy(test %>% aggregate_key(Sector/Stock, Value = mean(Value)))
acc4 %>% filter(is_aggregated(Sector))
## # A tibble: 2 × 12
## .model Sector Stock .type ME RMSE MAE MPE MAPE MASE RMSSE
## <chr> <chr*> <chr*> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 ets4 <aggregat… <aggregat… Test -8.76 13.6 11.8 -8.33 10.5 NaN NaN
## 2 mint <aggregat… <aggregat… Test -68.0 68.7 68.0 -58.1 58.1 NaN NaN
## # ℹ 1 more variable: ACF1 <dbl>
Accuracy metrics
fit <- myagg3 %>%
model(ets = ETS(Value)) %>%
reconcile(bottom_up = bottom_up(ets),
MinT = min_trace(ets),
top_down = top_down(ets),
middle_out = middle_out(ets),
)
fcst <- fit %>% forecast(h=12)
accuracy_table <- fcst %>% accuracy(test %>% aggregate_key(Sector/Stock, Value = mean(Value)))
kable(accuracy_table,
format = "markdown",
caption = "Model Accuracy")
Model Accuracy
| MinT |
Finance |
AMBC |
Test |
10.5847975 |
10.669803 |
10.584798 |
69.340092 |
69.340092 |
NaN |
NaN |
0.5246184 |
| MinT |
Finance |
BAC |
Test |
13.5690845 |
13.895308 |
13.569085 |
42.222383 |
42.222383 |
NaN |
NaN |
0.4097659 |
| MinT |
Finance |
|
Test |
0.6713416 |
1.973305 |
1.706177 |
2.232191 |
7.118058 |
NaN |
NaN |
0.4295048 |
| MinT |
Tech |
AAPL |
Test |
98.5561469 |
100.968130 |
98.556147 |
61.013536 |
61.013536 |
NaN |
NaN |
0.6962055 |
| MinT |
Tech |
MSFT |
Test |
170.8309234 |
173.964212 |
170.830923 |
61.620757 |
61.620757 |
NaN |
NaN |
0.7694010 |
| MinT |
Tech |
|
Test |
51.8221220 |
57.260127 |
51.822122 |
22.789969 |
22.789969 |
NaN |
NaN |
0.7403013 |
| MinT |
|
|
Test |
-68.0302807 |
68.666505 |
68.030281 |
-58.058031 |
58.058031 |
NaN |
NaN |
0.6207345 |
| bottom_up |
Finance |
AMBC |
Test |
3.6138914 |
3.856297 |
3.613891 |
23.146295 |
23.146295 |
NaN |
NaN |
0.5218961 |
| bottom_up |
Finance |
BAC |
Test |
-0.9006490 |
3.173922 |
2.674216 |
-3.781121 |
8.740353 |
NaN |
NaN |
0.4280993 |
| bottom_up |
Finance |
|
Test |
-20.7692981 |
20.857273 |
20.769298 |
-89.704067 |
89.704067 |
NaN |
NaN |
0.4596980 |
| bottom_up |
Tech |
AAPL |
Test |
-1.8925192 |
20.436583 |
17.530697 |
-2.778628 |
11.076385 |
NaN |
NaN |
0.6790635 |
| bottom_up |
Tech |
MSFT |
Test |
-23.4811672 |
37.999595 |
33.232276 |
-10.189793 |
13.095621 |
NaN |
NaN |
0.7497382 |
| bottom_up |
Tech |
|
Test |
-242.9386347 |
243.775623 |
242.938635 |
-114.840727 |
114.840727 |
NaN |
NaN |
0.6838691 |
| bottom_up |
|
|
Test |
-384.2316771 |
384.299233 |
384.231677 |
-323.536109 |
323.536109 |
NaN |
NaN |
0.3388331 |
| ets |
Finance |
AMBC |
Test |
3.6138914 |
3.856297 |
3.613891 |
23.146295 |
23.146295 |
NaN |
NaN |
0.5218961 |
| ets |
Finance |
BAC |
Test |
-0.9006490 |
3.173922 |
2.674216 |
-3.781121 |
8.740353 |
NaN |
NaN |
0.4280993 |
| ets |
Finance |
|
Test |
1.2869116 |
2.306127 |
1.915269 |
4.849127 |
7.829977 |
NaN |
NaN |
0.4596980 |
| ets |
Tech |
AAPL |
Test |
-1.8925192 |
20.436583 |
17.530697 |
-2.778628 |
11.076385 |
NaN |
NaN |
0.6790635 |
| ets |
Tech |
MSFT |
Test |
-23.4811672 |
37.999595 |
33.232276 |
-10.189793 |
13.095621 |
NaN |
NaN |
0.7497382 |
| ets |
Tech |
|
Test |
-19.9267478 |
29.795178 |
25.867061 |
-10.633164 |
12.877962 |
NaN |
NaN |
0.7163744 |
| ets |
|
|
Test |
-8.7556644 |
13.615830 |
11.807022 |
-8.333749 |
10.461152 |
NaN |
NaN |
0.6720512 |
| middle_out |
Finance |
AMBC |
Test |
9.3945091 |
9.490396 |
9.394509 |
61.452080 |
61.452080 |
NaN |
NaN |
0.5218961 |
| middle_out |
Finance |
BAC |
Test |
15.3749429 |
15.673273 |
15.374943 |
47.945954 |
47.945954 |
NaN |
NaN |
0.4280993 |
| middle_out |
Finance |
|
Test |
1.2869116 |
2.306127 |
1.915269 |
4.849127 |
7.829977 |
NaN |
NaN |
0.4596980 |
| middle_out |
Tech |
AAPL |
Test |
76.3695928 |
78.815333 |
76.369593 |
47.080026 |
47.080026 |
NaN |
NaN |
0.6671447 |
| middle_out |
Tech |
MSFT |
Test |
121.2686077 |
125.676600 |
121.268608 |
43.254332 |
43.254332 |
NaN |
NaN |
0.7701968 |
| middle_out |
Tech |
|
Test |
-19.9267478 |
29.795178 |
25.867061 |
-10.633164 |
12.877962 |
NaN |
NaN |
0.7163744 |
| middle_out |
|
|
Test |
-139.1635806 |
139.379119 |
139.163581 |
-117.637585 |
117.637585 |
NaN |
NaN |
0.4752063 |
| top_down |
Finance |
AMBC |
Test |
12.3158510 |
12.389158 |
12.315851 |
80.810630 |
80.810630 |
NaN |
NaN |
0.5217012 |
| top_down |
Finance |
BAC |
Test |
23.6001136 |
23.796132 |
23.600114 |
74.085781 |
74.085781 |
NaN |
NaN |
0.4296929 |
| top_down |
Finance |
|
Test |
12.4334241 |
12.580603 |
12.433424 |
52.631579 |
52.631579 |
NaN |
NaN |
0.4620918 |
| top_down |
Tech |
AAPL |
Test |
118.1920083 |
119.851802 |
118.192008 |
73.658504 |
73.658504 |
NaN |
NaN |
0.6728235 |
| top_down |
Tech |
MSFT |
Test |
198.7075960 |
202.028558 |
198.707596 |
71.753809 |
71.753809 |
NaN |
NaN |
0.7840639 |
| top_down |
Tech |
|
Test |
99.3346559 |
102.623782 |
99.334656 |
44.930570 |
44.930570 |
NaN |
NaN |
0.7512358 |
| top_down |
|
|
Test |
-8.7556644 |
13.615830 |
11.807022 |
-8.333749 |
10.461152 |
NaN |
NaN |
0.6720512 |
Comparison of Models
glance(m1)
## # A tibble: 10 × 10
## Stock .model sigma2 log_lik AIC AICc BIC MSE AMSE MAE
## <chr*> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 AAPL ets 0.00961 -195. 396. 396. 401. 90.9 188. 0.0830
## 2 AAPL bu 0.00961 -195. 396. 396. 401. 90.9 188. 0.0830
## 3 AMBC ets 3.86 -124. 255. 255. 260. 3.70 6.08 1.41
## 4 AMBC bu 3.86 -124. 255. 255. 260. 3.70 6.08 1.41
## 5 BAC ets 0.00899 -141. 289. 289. 294. 7.68 15.6 0.0757
## 6 BAC bu 0.00899 -141. 289. 289. 294. 7.68 15.6 0.0757
## 7 MSFT ets 0.00369 -207. 424. 426. 434. 176. 324. 0.0466
## 8 MSFT bu 0.00369 -207. 424. 426. 434. 176. 324. 0.0466
## 9 <aggregated> ets 0.00443 -172. 354. 355. 363. 33.9 63.0 0.0534
## 10 <aggregated> bu 0.00443 -172. 354. 355. 363. 33.9 63.0 0.0534
glance(m2)
## # A tibble: 14 × 11
## Sector Stock .model sigma2 log_lik AIC AICc BIC MSE AMSE
## <chr*> <chr*> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Finance AMBC ets2 3.86 -124. 255. 255. 260. 3.70 6.08
## 2 Finance AMBC md 3.86 -124. 255. 255. 260. 3.70 6.08
## 3 Finance BAC ets2 0.00899 -141. 289. 289. 294. 7.68 15.6
## 4 Finance BAC md 0.00899 -141. 289. 289. 294. 7.68 15.6
## 5 Finance <aggregat… ets2 4.73 -129. 264. 265. 270. 4.53 8.53
## 6 Finance <aggregat… md 4.73 -129. 264. 265. 270. 4.53 8.53
## 7 Tech AAPL ets2 0.00961 -195. 396. 396. 401. 90.9 188.
## 8 Tech AAPL md 0.00961 -195. 396. 396. 401. 90.9 188.
## 9 Tech MSFT ets2 0.00369 -207. 424. 426. 434. 176. 324.
## 10 Tech MSFT md 0.00369 -207. 424. 426. 434. 176. 324.
## 11 Tech <aggregat… ets2 0.00451 -198. 405. 407. 415. 112. 207.
## 12 Tech <aggregat… md 0.00451 -198. 405. 407. 415. 112. 207.
## 13 <aggregate… <aggregat… ets2 0.00443 -172. 354. 355. 363. 33.9 63.0
## 14 <aggregate… <aggregat… md 0.00443 -172. 354. 355. 363. 33.9 63.0
## # ℹ 1 more variable: MAE <dbl>
glance(m3)
## # A tibble: 14 × 11
## Sector Stock .model sigma2 log_lik AIC AICc BIC MSE AMSE
## <chr*> <chr*> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Finance AMBC ets3 3.86 -124. 255. 255. 260. 3.70 6.08
## 2 Finance AMBC td 3.86 -124. 255. 255. 260. 3.70 6.08
## 3 Finance BAC ets3 0.00899 -141. 289. 289. 294. 7.68 15.6
## 4 Finance BAC td 0.00899 -141. 289. 289. 294. 7.68 15.6
## 5 Finance <aggregat… ets3 4.73 -129. 264. 265. 270. 4.53 8.53
## 6 Finance <aggregat… td 4.73 -129. 264. 265. 270. 4.53 8.53
## 7 Tech AAPL ets3 0.00961 -195. 396. 396. 401. 90.9 188.
## 8 Tech AAPL td 0.00961 -195. 396. 396. 401. 90.9 188.
## 9 Tech MSFT ets3 0.00369 -207. 424. 426. 434. 176. 324.
## 10 Tech MSFT td 0.00369 -207. 424. 426. 434. 176. 324.
## 11 Tech <aggregat… ets3 0.00451 -198. 405. 407. 415. 112. 207.
## 12 Tech <aggregat… td 0.00451 -198. 405. 407. 415. 112. 207.
## 13 <aggregate… <aggregat… ets3 0.00443 -172. 354. 355. 363. 33.9 63.0
## 14 <aggregate… <aggregat… td 0.00443 -172. 354. 355. 363. 33.9 63.0
## # ℹ 1 more variable: MAE <dbl>
glance(m4)
## # A tibble: 14 × 11
## Sector Stock .model sigma2 log_lik AIC AICc BIC MSE AMSE
## <chr*> <chr*> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Finance AMBC ets4 3.86 -124. 255. 255. 260. 3.70 6.08
## 2 Finance AMBC mint 3.86 -124. 255. 255. 260. 3.70 6.08
## 3 Finance BAC ets4 0.00899 -141. 289. 289. 294. 7.68 15.6
## 4 Finance BAC mint 0.00899 -141. 289. 289. 294. 7.68 15.6
## 5 Finance <aggregat… ets4 4.73 -129. 264. 265. 270. 4.53 8.53
## 6 Finance <aggregat… mint 4.73 -129. 264. 265. 270. 4.53 8.53
## 7 Tech AAPL ets4 0.00961 -195. 396. 396. 401. 90.9 188.
## 8 Tech AAPL mint 0.00961 -195. 396. 396. 401. 90.9 188.
## 9 Tech MSFT ets4 0.00369 -207. 424. 426. 434. 176. 324.
## 10 Tech MSFT mint 0.00369 -207. 424. 426. 434. 176. 324.
## 11 Tech <aggregat… ets4 0.00451 -198. 405. 407. 415. 112. 207.
## 12 Tech <aggregat… mint 0.00451 -198. 405. 407. 415. 112. 207.
## 13 <aggregate… <aggregat… ets4 0.00443 -172. 354. 355. 363. 33.9 63.0
## 14 <aggregate… <aggregat… mint 0.00443 -172. 354. 355. 363. 33.9 63.0
## # ℹ 1 more variable: MAE <dbl>