| Title: | Simulate Time Series Diagnostics |
|---|---|
| Description: | These are tools that allow users to do time series diagnostics, primarily tests of unit root, by way of simulation. While there is nothing necessarily wrong with the received wisdom of critical values generated decades ago, simulation provides its own perks. Not only is simulation broadly informative as to what these various test statistics do and what are their plausible values, simulation provides more flexibility for assessing unit root by way of different thresholds or different hypothesized distributions. |
| Authors: | Steven Miller [aut, cre]
|
| Maintainer: | Steven Miller <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.0 |
| Built: | 2024-12-21 03:44:30 UTC |
| Source: | CRAN |
spp_test() provides a simulation approach to assessing
unit root in a time series by way of the Phillips-Perron test. It takes a
vector and performs three Phillips-Perron tests (no drift, no trend; drift, no
trend; drift and trend) and calculates both rho and tau statistics as one
normally would. Rather than interpolate or approximate a *p*-value, it
simulates some user-specified number of Phillips-Perron tests of a known,
white-noise time series matching the length of the time series the user
provides. This allows the user to make assessments of non-stationarity or
stationarity by way of simulation rather than approximation from received
critical values by way of books or tables some years out of date.
spp_test(x, lag_short = TRUE, n_sims = 1000, sim_hyp = "nonstationary")spp_test(x, lag_short = TRUE, n_sims = 1000, sim_hyp = "nonstationary")
x |
a vector |
lag_short |
logical, defaults to |
n_sims |
the number of simulations for calculating an interval or distribution of test statistics of a white-noise time series. Defaults to 1,000. |
sim_hyp |
can be either "stationary" or "nonstationary". If "stationary" (the default), the function runs Phillips-Perron tests on simulated stationary (pure white noise) data. This allows the user to assess compatibility/plausibility of the test statistic against a distribution of test statistics that are known to be pure white noise (in expectation). If "nonstationary", the function generates three different data sets of a pure random walk, a random walk with a drift, and a random walk with a drift and trend. It then runs Phillips-Perron tests on all those. This allows the user to assess the compatibility/plausibility of their test statistics with data that are known to be nonstationary in some form. |
Some knowledge of Augmented Dickey-Fuller and the Phillips-Perron procedure is assumed here. Generally, the Phillips-Perron test purports to build on the Augmented Dickey-Fuller procedure through two primary means. The first is relaxing the need to specify or assume lag structures ad hoc or ex ante. Only a short-term lag or long-term lag are necessary. The second is that its robust to various forms of heteroskedasticity in the error term.
The short-term and long-term lags follow the convention introduced in the Phillips-Perron test. The short-term lag uses the default number of Newey-West lags, defined as the floor of 4*(n/100)^.25 where 'n' is the length of the time series. The long-term lag substitutes 4 for 12 in this equation.
This function specifies three different types of tests: 1) no drift, no trend, 2) drift, no trend, and 3) drift and trend. In the language of the 'lm()' function, the first is 'lm(y ~ ly - 1)' where 'y' is the value of 'y' and 'ly' is its first-order lag. The second test is 'lm(y ~ ly)', intuitively suggesting the *y*-intercept in this equation is the "drift". The third would be 'lm(y ~ ly + t)' with 't' being a simple integer that increases by 1 for each observation (i.e. a time-trend).
There are two types of statistics in the Phillips-Perron test: rho and tau. Of the two, tau is the more intuitive statistic and compares favorably to its corollary statistic in the Augmented Dickey-Fuller test. It's why you'll typically see tau reported as the statistic of interest in other implementations. rho has its utility for more advanced diagnostics, though. Both are calculated in this function, though tau is the default statistic.
None of this is meant to discourage the use of Fuller (1976) or its various reproductions for the sake of diagnosing stationarity or non-stationary, and I will confess their expertise on these matters outpaces mine. Consider the justification for this function to be largely philosophical and/or experimental. Why not simulate it? It's not like time or computing power are huge issues anymore.
This is always awkwardly stated, but it's a good reminder that the classic Dickey-Fuller statistics are mostly intended to come back negative. That's not always the case, to be clear, but it is the intended case. You assess the statistic by "how negative" it is. Stationary time series will produce test statistics more negative ("smaller") than those produced by non-stationary time series. In a way, this makes the hypotheses implicitly one-tailed (to use that language).
This function removes missing values from the vector before calculating test statistics.
spp_test() returns a list of length 3. The first element
in the list is a matrix of rho statistics and tau statistics calculated by
the Phillips-Perron test. The second element is a data frame of the simulated
rho and tau statistics of either a known white-noise time series or three
different non-stationary time series (pure random walk, random walk with
drift, random walk with drift and trend). The third element is some
attributes about the procedure for post-processing.
Steven V. Miller
a <- rnorm(25) # white noise b <- cumsum(a) # random walk spp_test(a, n_sims = 25) spp_test(b, n_sims = 25)a <- rnorm(25) # white noise b <- cumsum(a) # random walk spp_test(a, n_sims = 25) spp_test(b, n_sims = 25)
ur_summary() provides a summary of the unit root tests
included in this package.
ur_summary(obj, pp_stat = "tau", ...)ur_summary(obj, pp_stat = "tau", ...)
obj |
the object to be summarized, of class 'spp_test' |
pp_stat |
the statistic to be summarized: either "tau" or "rho" |
... |
additional argument, currently ignored |
This function makes ample use of the "attributes" element in the list produced by the unit root simulations.
ur_summary() produces console output that offers a summary
assessment about the presence of a unit root based on your simulations.
Steven V. Miller
A data frame on the USD/SEK exchange rate (i.e. how many Swedish crowns does one dollar get you).
USDSEKUSDSEK
A data frame with 3905 observations on the following 2 variables.
datea date
closethe exchange rate at the close of trading
Data come by way of quantmod.