Load packages and data

library(fpp3)
library(readxl)
# install and load any package necessary

Questions

Exercise 1

tesla_stock <- read_excel("C:\\Users\\Zacha\\OneDrive\\Documents\\Tesla Stock.xls")

tesla_stock
## # A tibble: 253 x 2
##    Date                Close
##    <dttm>              <dbl>
##  1 2021-11-16 00:00:00  352.
##  2 2021-11-17 00:00:00  363.
##  3 2021-11-18 00:00:00  365.
##  4 2021-11-19 00:00:00  379.
##  5 2021-11-22 00:00:00  386.
##  6 2021-11-23 00:00:00  370.
##  7 2021-11-24 00:00:00  372 
##  8 2021-11-26 00:00:00  361.
##  9 2021-11-29 00:00:00  379.
## 10 2021-11-30 00:00:00  382.
## # ... with 243 more rows
## # i Use `print(n = ...)` to see more rows
tesla.ts <- tesla_stock %>%
  mutate(row = row_number()) %>%
  as_tsibble(index = row) %>%
  slice(210:253)

autoplot(tesla.ts)
## Plot variable not specified, automatically selected `.vars = Close`

#There's a clear downward trend to the data. Let's try taking the difference. 

tesla.diff <- tesla.ts %>%
  mutate(Close = difference(Close))

tesla.diff %>%
  autoplot()
## Plot variable not specified, automatically selected `.vars = Close`
## Warning: Removed 1 row(s) containing missing values (geom_path).

#That looks a lot better. Let's check for white-noise. 

tesla.ts %>%
  features(Close,ljung_box, lag = 10)
## # A tibble: 1 x 2
##   lb_stat lb_pvalue
##     <dbl>     <dbl>
## 1    153.         0
#ljung_box of 0 means our residuals are indistinguishable from white noise. 

tesla.ts %>%
  ACF(difference(Close)) %>%
  autoplot()

#No autocorrelation.

tesla.ts %>%
  PACF(difference(Close)) %>%
  autoplot()

#No partial autocorrelation either. 

#So for my ARIMA I'm looking at a (0,1,0)

tesla.fit <- tesla.ts %>% 
  model(ARIMA(Close~pdq(0,1,0)))

tesla.fc <- tesla.fit %>% 
  forecast(h=1)

tesla.fc
## # A fable: 1 x 4 [1]
## # Key:     .model [1]
##   .model                        row      Close .mean
##   <chr>                       <dbl>     <dist> <dbl>
## 1 ARIMA(Close ~ pdq(0, 1, 0))   254 N(184, 78)  184.
hilo(tesla.fc)
## # A tsibble: 1 x 6 [1]
## # Key:       .model [1]
##   .model      row      Close .mean                  `80%`                  `95%`
##   <chr>     <dbl>     <dist> <dbl>                 <hilo>                 <hilo>
## 1 ARIMA(Cl~   254 N(184, 78)  184. [172.8965, 195.5282]80 [166.9062, 201.5184]95
gg_tsresiduals(tesla.fit)

#Residuals look pretty good. I'm happy with this forecast. Now for the fun part. 


#I might let the NAIVE model decide my destiny. 


tesla.naive <- tesla.ts %>%
  model('Simple' = ETS(Close ~ error("A") + trend("N") + season("N")))

tesla.naive %>%
  forecast(h=1) %>%
  autoplot(tesla.ts)

tesla.naive %>%
  forecast(h=1) %>%
  hilo()
## # A tsibble: 1 x 6 [1]
## # Key:       .model [1]
##   .model   row      Close .mean                  `80%`                  `95%`
##   <chr>  <dbl>     <dist> <dbl>                 <hilo>                 <hilo>
## 1 Simple   254 N(187, 85)  187. [175.4789, 199.1269]80 [169.2196, 205.3861]95
#An official prediction of 187 from the NAIVE model.

THE GUESS: My ARIMA model predicted 184 as the closing price tomorrow and the NIAVE predicted 187. Everyone seems to think it’s going to decrease so I am going to just take a shot in the dark here and say $191 with a prediction interval of 169.2196 - 205.3861 which is from my ARIMA model.