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Subsample IVX Tests for Episodic Predictability

Source: R/ivx-episodic.R
ivx_episodic.Rd

Tests for "pockets" of predictability using the suprema of sequences of subsample IVX statistics (Demetrescu et al., 2023, Section 3.2; Demetrescu et al., 2022). For each window the IVX statistic is computed from the window's observations with the full-sample instrument (eqs 15-17); the test statistics are the maximum (right-tailed), minimum (left-tailed) and maximum squared (two-sided) t-ratio over the sequence for a single predictor, and the maximum Wald statistic for several predictors (Remark 11). P-values are obtained by wild bootstrap (Algorithms 1-2), which the paper shows to be asymptotically valid for these sup-functionals.

Usage

ivx_episodic(
  object,
  scheme = c("rolling", "forward", "backward"),
  window = 0.2,
  robust = FALSE,
  B = 999,
  type = c("frwb", "rwb"),
  ar_max = 5,
  dist = c("rademacher", "normal"),
  seed = NULL,
  cores = 1L
)

# S3 method for class 'ivx_episodic'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

object

an object of class "ivx" fitted with horizon = 1.

scheme

"rolling" windows of fixed width, "forward" recursive windows starting at the first observation, or "backward" recursive windows ending at the last observation.

window

fraction of the sample: the window width for "rolling", the warm-in fraction \(\tau_L\) for "forward", and the latest start \(\tau_U\) for "backward".

robust

logical; use Eicker-White standard errors in the subsample statistics.

B

number of bootstrap replications.

type

bootstrap scheme, see ivx_boot(). The default fixed regressor wild bootstrap is the scheme used by Demetrescu et al. (2022).

ar_max

maximum lag order of the (vector) autoregression fitted to the regressors by the RWB scheme; the order is selected by BIC (Remark 24).

dist

distribution of the wild multipliers.

seed

optional integer seed. With cores > 1 the L'Ecuyer-CMRG streams of the parallel package are used, so results are reproducible for a given seed and cores but differ from the serial run.

cores

number of CPU cores. Uses forking on Unix and a PSOCK cluster on Windows (the package must be installed for the workers to load it).

x

an object of class "ivx_episodic".

digits

minimal number of significant digits.

...

unused.

Value

an object of class "ivx_episodic": the observed sequence (sequence, one row per window with its start/end index and statistics), the sup statistics (statistic) and their bootstrap p-values (p.value), plus the bootstrap draws (boot).

References

Demetrescu, M., Georgiev, I., Rodrigues, P. M. M., & Taylor, A. M. R. (2022). Testing for episodic predictability in stock returns. Journal of Econometrics, 227(1), 85-113.

Demetrescu, M., Georgiev, I., Rodrigues, P. M. M., & Taylor, A. M. R. (2023). Extensions to IVX methods of inference for return predictability. Journal of Econometrics, 237(2), 105271.

Examples

mod <- ivx(Ret ~ DP, data = kms)
ivx_episodic(mod, scheme = "rolling", window = 0.2, B = 99, seed = 1)
#> 
#> Call:
#> ivx(formula = Ret ~ DP, data = kms, horizon = 1)
#> 
#> Subsample IVX tests, rolling scheme (window = 0.2), 827 windows
#> Fixed regressor wild bootstrap, B = 99
#> 
#>                         statistic bootstrap p
#> sup t   (H1: beta > 0)      2.921       0.202
#> inf t   (H1: beta < 0)    -0.4166       1.000
#> sup t^2 (H1: beta != 0)     8.533       0.303
#>