For our analysis we are going to use the
datasets::EuStockMarkets dataset, which contains the daily
closing prices of four major European stock indices: Germany DAX,
Switzerland SMI, France CAC, and UK FTSE (see
?EuStockMarkets). The data are sampled in business time,
i.e., weekends and holidays are omitted. In this particular exercise we
want to focus on weekly observations. To do so we aggregate to a weekly
frequency and reduce the number of observations from 1860 to 372.
stocks <- aggregate(EuStockMarkets, nfrequency = 52, mean)Estimation
We estimate the above series using the recursive Augmented Dickey-Fuller test with 1 lag.
est_stocks <- radf(stocks, lag = 1)Analysis
The summary will print the test statistic and the critical values for
10%, 5% and 1% significance level. When cv is omitted,
summary()/diagnostics()/datestamp()/autoplot()
fetch precomputed Monte Carlo critical values for this
(n, lag) from a shared store (lags 0-4, samples up to 4000;
needs network access the first time, cached on disk after). Here we
simulate them locally with radf_mc_cv() instead, and pass
the result via cv to every downstream call – the offline
route, and the one to use for other lags or larger samples.
cv_stocks <- radf_mc_cv(NROW(stocks), lag = 1)
summary(est_stocks, cv = cv_stocks)
#>
#> ── Summary (minw = 38, lag = 1) ────────────────── Monte Carlo (nboot = 1000) ──
#>
#> DAX :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf 1.45 -0.440 -0.0429 0.537
#> 2 sadf 4.95 1.23 1.54 2.06
#> 3 gsadf 5.18 2.13 2.38 3.00
#>
#> SMI :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf 1.77 -0.440 -0.0429 0.537
#> 2 sadf 4.28 1.23 1.54 2.06
#> 3 gsadf 4.49 2.13 2.38 3.00
#>
#> CAC :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf 0.987 -0.440 -0.0429 0.537
#> 2 sadf 2.91 1.23 1.54 2.06
#> 3 gsadf 2.97 2.13 2.38 3.00
#>
#> FTSE :
#> # A tibble: 3 × 5
#> stat tstat `90` `95` `99`
#> <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf 0.194 -0.440 -0.0429 0.537
#> 2 sadf 2.56 1.23 1.54 2.06
#> 3 gsadf 2.67 2.13 2.38 3.00It seems that all stocks exhibit exuberant behaviour but we can also
verify it using diagnostics(). This function is
particularly useful when we deal a large number of series.
diagnostics(est_stocks, cv = cv_stocks)
#>
#> ── Diagnostics (option = gsadf) ───────────────────────────────── Monte Carlo ──
#>
#> DAX: Rejects H0 at the 1% significance level
#> SMI: Rejects H0 at the 1% significance level
#> CAC: Rejects H0 at the 5% significance level
#> FTSE: Rejects H0 at the 5% significance levelIf we need to know the exact period of exuberance we can do so with
the function datestamp(). datestamp() works in
a similar manner with summary() and
diagnostics().
# Minimum duration of an explosive period
rot = psy_ds(stocks) # log(n) ~ rule of thumb
dstamp_stocks <- datestamp(est_stocks, cv = cv_stocks, min_duration = rot)
dstamp_stocks
#>
#> ── Datestamp (min_duration = 6) ───────────────────────────────── Monte Carlo ──
#>
#> DAX :
#> Start Peak End Duration Signal Ongoing
#> 1 1997-02-10 1997-08-05 1997-11-04 38 positive FALSE
#> 2 1998-01-27 1998-07-22 1998-08-19 29 positive FALSE
#>
#> SMI :
#> Start Peak End Duration Signal Ongoing
#> 1 1993-12-02 1994-02-03 1994-02-17 11 positive FALSE
#> 2 1997-04-14 1997-07-15 1997-09-02 20 positive FALSE
#> 3 1997-09-09 1997-10-07 1997-11-04 8 positive FALSE
#> 4 1997-11-25 1998-04-07 1998-08-19 39 positive TRUE
#>
#> CAC :
#> Start Peak End Duration Signal Ongoing
#> 1 1997-07-08 1997-08-05 1997-08-19 6 positive FALSE
#> 2 1998-03-10 1998-07-15 1998-08-12 22 positive FALSE
#>
#> FTSE :
#> Start Peak End Duration Signal Ongoing
#> 1 1997-07-08 1997-08-12 1997-09-02 8 positive FALSE
#> 2 1997-09-23 1997-10-07 1997-11-04 6 positive FALSE
#> 3 1998-02-10 1998-04-14 1998-06-24 19 positive FALSEWe can extract the datestamp as a dummy variable 1 = Exuberance, 0 = No exuberance.
dummy <- attr(dstamp_stocks, "dummy")
tail(dummy)
#> DAX SMI CAC FTSE
#> 367 1 1 1 1
#> 368 1 1 1 1
#> 369 1 1 1 1
#> 370 1 1 1 0
#> 371 1 1 0 0
#> 372 0 1 0 0datestamp() is not the only way to get dates out of the
package, and the other two answer different questions rather than being
alternate ways to get the same answer: the dating_*()
family (vignette("dating-methods")) fits an explicit regime
model to date a bubble you already believe is there, instead of testing
whether one exists; the monitor()/monitor_*()
family (vignette("monitoring")) does real-time detection,
watching new observations one at a time rather than dating a finished
sample. See vignette("naming-and-analysis") for how every
function in the package relates to this one.
Plotting
The autoplot function returns a faceted ggplot2 object
for all the series that reject the null hypothesis at 5% significance
level.
autoplot(est_stocks, cv = cv_stocks)
Finally, we can plot just the periods the periods of exuberance. Plotting datestamp object is particularly useful when we have a lot of series, and we are interested to identify explosive patterns in all of them.
