Models2

Model Google’s stock price.

library(pacman)
p_load(tidyverse, fpp3)

Re-index based on trading days

google_stock <- gafa_stock |>
  filter(Symbol == "GOOG", year(Date) >= 2015) |>
  mutate(day = row_number()) |>
  update_tsibble(index = day, regular = TRUE)

google_stock

ABCDEFGHIJ0123456789

Symbol <chr>	Date <date>	Open <dbl>	High <dbl>	Low <dbl>	Close <dbl>	Adj_Close <dbl>	Volume <dbl>	day <int>
GOOG	2015-01-02	526.1147	528.3624	521.2316	521.9377	521.9377	1447600	1
GOOG	2015-01-05	520.3962	521.4604	510.2520	511.0576	511.0576	2059800	2
GOOG	2015-01-06	512.1815	513.3500	498.3078	499.2128	499.2128	2899900	3
GOOG	2015-01-07	504.2252	504.4679	496.9154	498.3575	498.3575	2065100	4
GOOG	2015-01-08	495.2645	500.7245	488.3128	499.9289	499.9289	3353600	5
GOOG	2015-01-09	501.9975	502.1566	492.0821	493.4545	493.4545	2069400	6
GOOG	2015-01-12	492.2312	493.2616	484.8916	489.8543	489.8543	2322400	7
GOOG	2015-01-13	496.1099	500.2272	489.6952	493.4644	493.4644	2370500	8
GOOG	2015-01-14	491.9428	500.4759	490.3018	498.1288	498.1288	2235700	9
GOOG	2015-01-15	502.8030	502.9124	495.0358	499.0437	499.0437	2715800	10

Next

123456

...

101

Previous

1-10 of 1,006 rows

Filter the year of interest

google_2015 <- google_stock |> filter(year(Date) == 2015)
google_2015 

ABCDEFGHIJ0123456789

Symbol <chr>	Date <date>	Open <dbl>	High <dbl>	Low <dbl>	Close <dbl>	Adj_Close <dbl>	Volume <dbl>	day <int>
GOOG	2015-01-02	526.1147	528.3624	521.2316	521.9377	521.9377	1447600	1
GOOG	2015-01-05	520.3962	521.4604	510.2520	511.0576	511.0576	2059800	2
GOOG	2015-01-06	512.1815	513.3500	498.3078	499.2128	499.2128	2899900	3
GOOG	2015-01-07	504.2252	504.4679	496.9154	498.3575	498.3575	2065100	4
GOOG	2015-01-08	495.2645	500.7245	488.3128	499.9289	499.9289	3353600	5
GOOG	2015-01-09	501.9975	502.1566	492.0821	493.4545	493.4545	2069400	6
GOOG	2015-01-12	492.2312	493.2616	484.8916	489.8543	489.8543	2322400	7
GOOG	2015-01-13	496.1099	500.2272	489.6952	493.4644	493.4644	2370500	8
GOOG	2015-01-14	491.9428	500.4759	490.3018	498.1288	498.1288	2235700	9
GOOG	2015-01-15	502.8030	502.9124	495.0358	499.0437	499.0437	2715800	10

Next

123456

...

26

Previous

1-10 of 252 rows

Fit the models

google_fit <- google_2015 |>
  model(
    Mean = MEAN(Close),
    `Naïve` = NAIVE(Close),
    Drift = NAIVE(Close ~ drift())
  )
google_fit 

ABCDEFGHIJ0123456789

Symbol <chr>	Mean <lst_mdl>	Naïve <lst_mdl>	Drift <lst_mdl>
GOOG	<lst_mdl>	<lst_mdl>	<lst_mdl>

1 row

Produce forecasts for the trading days in January 2016

google_jan_2016 <- google_stock |>
  filter(yearmonth(Date) == yearmonth("2016 Jan"))

google_fc <- google_fit |> 
  forecast(new_data = google_jan_2016)
google_fc

ABCDEFGHIJ0123456789

Symbol <chr>	.model <chr>	day <int>	Close <dist>	.mean <dbl>	Date <date>	Open <dbl>	High <dbl>	Low <dbl>	Adj_Close <dbl>
GOOG	Mean	253	<dist>	601.5505	2016-01-04	743.00	744.060	731.258	741.84
GOOG	Mean	254	<dist>	601.5505	2016-01-05	746.45	752.000	738.640	742.58
GOOG	Mean	255	<dist>	601.5505	2016-01-06	730.00	747.180	728.920	743.62
GOOG	Mean	256	<dist>	601.5505	2016-01-07	730.31	738.500	719.060	726.39
GOOG	Mean	257	<dist>	601.5505	2016-01-08	731.45	733.230	713.000	714.47
GOOG	Mean	258	<dist>	601.5505	2016-01-11	716.61	718.855	703.540	716.03
GOOG	Mean	259	<dist>	601.5505	2016-01-12	721.68	728.750	717.317	726.07
GOOG	Mean	260	<dist>	601.5505	2016-01-13	730.85	734.740	698.610	700.56
GOOG	Mean	261	<dist>	601.5505	2016-01-14	705.38	721.925	689.100	714.72
GOOG	Mean	262	<dist>	601.5505	2016-01-15	692.29	706.740	685.370	694.45

Next

123456

Previous

1-10 of 57 rows | 1-10 of 11 columns

Plot the forecasts

google_fc |>
  autoplot(google_2015, level = NULL) +
  autolayer(google_jan_2016, Close, color = "black") +
  labs(x = "Day", y = "Closing Price (US$)",
       title = "Google stock prices (Jan 2015 - Jan 2016)") +
  guides(colour = guide_legend(title = "Forecast"))

augment(google_fit)

ABCDEFGHIJ0123456789

Symbol <chr>	.model <chr>	day <int>	Close <dbl>	.fitted <dbl>	.resid <dbl>	.innov <dbl>
GOOG	Mean	1	521.9377	601.5505	-7.961280e+01	-7.961280e+01
GOOG	Mean	2	511.0576	601.5505	-9.049293e+01	-9.049293e+01
GOOG	Mean	3	499.2128	601.5505	-1.023377e+02	-1.023377e+02
GOOG	Mean	4	498.3575	601.5505	-1.031930e+02	-1.031930e+02
GOOG	Mean	5	499.9289	601.5505	-1.016217e+02	-1.016217e+02
GOOG	Mean	6	493.4545	601.5505	-1.080960e+02	-1.080960e+02
GOOG	Mean	7	489.8543	601.5505	-1.116962e+02	-1.116962e+02
GOOG	Mean	8	493.4644	601.5505	-1.080861e+02	-1.080861e+02
GOOG	Mean	9	498.1288	601.5505	-1.034218e+02	-1.034218e+02
GOOG	Mean	10	499.0437	601.5505	-1.025068e+02	-1.025068e+02

Next

123456

...

76

Previous

1-10 of 756 rows

Residual diagnostics

A good forecasting method will yield innovation residuals with the following properties:

1. The innovation residuals are uncorrelated. If there are correlations between innovation residuals, then there is information left in the residuals which should be used in computing forecasts.
2. The innovation residuals have zero mean. If they have a mean other than zero, then the forecasts are biased.
3. The innovation residuals have constant variance.
4. The innovation residuals are normally distributed.

autoplot(google_2015, Close) +
  labs(x = "Day", y = "Closing Price (US$)",
       title = "Google Stock in 2015")

Fit the Naive model (jus t the mean) and augment the dataset with the residuals and innovations.

aug <- google_2015 |>
  model(NAIVE(Close)) |>
  augment()

autoplot(aug, .innov) +
  labs(x = "Day", y = "Residual",
       title = "Residuals from naïve method")

Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_line()`).

Normal?

aug |>
  ggplot(aes(x = .innov)) +
  geom_histogram() +
  labs(title = "Histogram of residuals")

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Warning: Removed 1 row containing non-finite outside the scale range
(`stat_bin()`).

aug |>
  ACF(.innov) |>
  autoplot() +
  labs(title = "ACF of residuals")

google_2015 |>
  model(NAIVE(Close)) |>
  gg_tsresiduals()

Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_line()`).

Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_point()`).

Warning: Removed 1 row containing non-finite outside the scale range
(`stat_bin()`).

Portmanteau test

From a French word describing a suitcase or coat rack carrying several items of clothing.

Test if there is at least one lagged autocorrelation is different from zero.

Box-Pierce

aug |> features(.innov, box_pierce, lag = 10)

ABCDEFGHIJ0123456789

Symbol <chr>	.model <chr>	bp_stat <dbl>	bp_pvalue <dbl>
GOOG	NAIVE(Close)	7.744517	0.6537761

1 row

Ljung-Box

aug |> features(.innov, ljung_box, lag = 10)

ABCDEFGHIJ0123456789

Symbol <chr>	.model <chr>	lb_stat <dbl>	lb_pvalue <dbl>
GOOG	NAIVE(Close)	7.914143	0.6372231

1 row