For our analysis we are going to use thedatasets::EuStockMarkets dataset, which contains the dailyclosing 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 wewant to focus on weekly observations. To do so we aggregate to a weeklyfrequency and reduce the number of observations from 1860 to 372.
We estimate the above series using the recursive AugmentedDickey-Fuller test with 1 lag.
The summary will print the test statistic and the critical values for10%, 5% and 1% significance level. The package provides simulatedcritical values for up to 600 observations, so we use them by omittingthecv argument in thesummary function.
summary(est_stocks)#>#> ── Summary (minw = 38, lag = 1) ─────────────────── Monte Carlo (nrep = 2000) ──#>#> DAX :#> # A tibble: 3 × 5#> stat tstat `90` `95` `99`#> <fct> <dbl> <dbl> <dbl> <dbl>#> 1 adf 1.45 -0.437 -0.0900 0.511#> 2 sadf 4.95 1.14 1.42 2.04#> 3 gsadf 5.18 1.90 2.14 2.60#>#> SMI :#> # A tibble: 3 × 5#> stat tstat `90` `95` `99`#> <fct> <dbl> <dbl> <dbl> <dbl>#> 1 adf 1.77 -0.437 -0.0900 0.511#> 2 sadf 4.28 1.14 1.42 2.04#> 3 gsadf 4.49 1.90 2.14 2.60#>#> CAC :#> # A tibble: 3 × 5#> stat tstat `90` `95` `99`#> <fct> <dbl> <dbl> <dbl> <dbl>#> 1 adf 0.987 -0.437 -0.0900 0.511#> 2 sadf 2.91 1.14 1.42 2.04#> 3 gsadf 2.97 1.90 2.14 2.60#>#> FTSE :#> # A tibble: 3 × 5#> stat tstat `90` `95` `99`#> <fct> <dbl> <dbl> <dbl> <dbl>#> 1 adf 0.194 -0.437 -0.0900 0.511#> 2 sadf 2.56 1.14 1.42 2.04#> 3 gsadf 2.67 1.90 2.14 2.60It seems that all stocks exhibit exuberant behaviour but we can alsoverify it usingdiagnostics(). This function isparticularly useful when we deal a large number of series.
diagnostics(est_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 1% significance level#> FTSE: Rejects H0 at the 1% significance levelIf we need to know the exact period of exuberance we can do so withthe functiondatestamp().datestamp() works ina similar manner withsummary() anddiagnostics(). The user still has to specify the criticalvalues, however we can still utilize the package’s critical values byleaving the cv-argument blank.
# Minimum duration of an explosive periodrot=psy_ds(stocks)# log(n) ~ rule of thumbdstamp_stocks<-datestamp(est_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 30 positive TRUE#>#> 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 1997-10-07 1997-11-04 17 positive FALSE#> 2 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.
Theautoplot function returns a faceted ggplot2 objectfor all the series that reject the null hypothesis at 5% significancelevel.
Finally, we can plot just the periods the periods of exuberance.Plotting datestamp object is particularly useful when we have a lot ofseries, and we are interested to identify explosive patterns in all ofthem.