Testing constancy of unconditional variance in volatility models by misspecification and specification tests

Abstract

Abstract:The topic of this paper is testing the hypothesis of constant unconditional variance in GARCH models against the alternative that the unconditional variance changes deterministically over time. Tests of this hypothesis have previously been performed as misspecification tests after fitting a GARCH model to the original series. It is found by simulation that the positive size distortion present in these tests is a function of the kurtosis of the GARCH process. Adjusting the size by numerical methods is considered. The possibility of testing the constancy of the unconditional variance before fitting a GARCH model to the data is discussed. The power of the ensuing test is vastly superior to that of the misspecification test and the size distortion minimal. The test has reasonable power already in very short time series. It would thus serve as a test of constant variance in conditional mean models. An application to exchange rate returns is included.

The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016

“…ji > 0 for k = 1; :::; r j and j = 1; :::; S: This de…nition imposes restrictions on ! ji ; i = 1; :::; r j : For the individual unit s it conforms to the one in Silvennoinen and Teräsvirta (2016). A di¤erence compared to that de…nition is that is 2…”

“…As in the case of the time-varying intercept, the testing problem is nonstandard. It has been already discussed in Silvennoinen and Teräsvirta (2016). Their solution is to circumvent the identi…cation problem by approximating the transition function (8) by a Taylor expansion around the null hypothesis…”

“…Constancy of error variances is tested as in Silvennoinen and Teräsvirta (2016). The di¤erence is that because of seasonal heteroskedasticity, the test is conducted separately for each month.…”

Comparing long monthly Chinese and selected European temperature series using the Vector Seasonal Shifting Mean and Covariance Autoregressive model

“…nji > 0 for q = 1; :::; r nj ; n = 1; :::; N; and j = 1; :::; S: This de…nition imposes restrictions on ! nji ; i = 1; :::; r nj : For the individual season s it conforms to the one in Silvennoinen and Teräsvirta (2016). To …x notation, let (v)…”

Testing for an Omitted Multiplicative Long-Term Component in GARCH Models

“…In this model, a short-term GARCH component fluctuates around a smooth long-term component that is driven by macroeconomic conditions. For further multiplicative component GARCH models see, for example, Feng (2004), Engle and Rangel (2008), Amado andTeräsvirta (2013, 2017) and Silvennoinen and Teräsvirta (2016). A recent survey on multiplicative component models and their properties is provided by Amado et al (2018).…”