testL {ACV}

Test equality of out-of-sample losses of two algorithms

Description

Function testL() tests the null hypothesis of equal predictive ability of algorithm1 and algorithm2 on time series y. By default, it uses the optimal weighting scheme which exploits also the in-sample performance in order to deliver more power than the conventional tests.

Usage

testL(
  y,
  algorithm1,
  algorithm2,
  m,
  h = 1,
  v = 1,
  xreg = NULL,
  lossFunction = function(y, yhat) {     (y - yhat)^2 },
  method = "optimal",
  test = "Diebold-Mariano",
  Ha = "!=0",
  Phi = NULL,
  bw = NULL,
  groups = 2,
  rhoLimit = 0.99,
  ...
)

Arguments

y

Univariate time-series object.

algorithm1

First algorithm which is to be applied to the time-series. The object which the algorithm produces should respond to fitted and forecast methods. Alternatively in the case of more complex custom algorithms, the algorithm may be a function which takes named arguments ⁠("yInSample", "yOutSample", "h")⁠ or ⁠("yInSample", "yOutSample", "h", "xregInSample", "xregOutSample")⁠ as inputs and produces a list with named elements ⁠("yhatInSample", "yhatOutSample")⁠ containing vectors of in-sample and out-of-sample forecasts.

algorithm2

Second algorithm. See above.

m

Length of the window on which the algorithm should be trained.

h

Number of predictions made after a single training of the algorithm.

v

Number of periods by which the estimation window progresses forward once the predictions are generated.

xreg

Matrix of exogenous regressors supplied to the algorithm (if applicable).

lossFunction

Loss function used to compute contrasts (defaults to squared error).

method

Can be set to either "optimal" for the test which optimally utilizes also the in-sample performance or "convetional" for the conventional test.

test

Type of the test which is to be executed. Can attain values "Diebold-Mariano" for the canonical test of equal predictive ability or "Ibragimov-Muller" for the sub-sampling t-test.

Ha

Alternative hypothesis. Can attain values "!=0" for two sided test or "<0" and ">0" for one sided tests.

Phi

User can also directly supply Phi=Phi1-Phi2; the matrix of contrasts differentials produced by tsACV. In this case parameters: y, algorithm, m, h, v, xreg, lossFunction are ignored.

bw

Applicable to "Diebold-Mariano" test. Bandwidth for the long run variance estimator. If NULL, bw is selected according to (3/4)*n^(1/3).

groups

Applicable to "Ibragimov-Muller" test. The number of groups to which the data is to be divided.

rhoLimit

Parameter rhoLimit limits to the absolute value of the estimated rho coefficient. This is useful as estimated values very close to 1 might cause instability.

...

Other parameters passed to algorithms.

Value

List containing loss differential estimate and associated p-value along with some other auxiliary information like the matrix of contrasts differentials Phi and the weights used for computation.

Examples

set.seed(1)
y <- rnorm(40)
m <- 36
h <- 1
v <- 1
algorithm1 <- function(y) {
  forecast::Arima(y, order = c(1, 0, 0))
}
algorithm2 <- function(y) {
  forecast::Arima(y, order = c(2, 0, 0))
}
testL(y, algorithm1, algorithm2, m = m, h = h, v = v)