Denis Kwiatkowski

Bio: Denis Kwiatkowski is an academic researcher from Central Michigan University. The author has contributed to research in topics: Order of integration & KPSS test. The author has an hindex of 3, co-authored 4 publications receiving 10096 citations.

Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?

Abstract: The standard conclusion that is drawn from this empirical evidence is that many or most aggregate economic time series contain a unit root. However, it is important to note that in this empirical work the unit root is set up as the null hypothesis testing is carried out ensures that the null hypothesis is accepted unless there is strong evidence against it. Therefore, an alternative explanation for the common failure to reject a unit root is simply that most economic time series are not very informative about whether or not there is a unit root; or, equivalently, that standard unit root tests are not very powerful against relevant alternatives.

Dickey-Fuller tests with trend

Abstract: The Dickey-Fuller [rcirc]τ and [pcirc]τ tests are based on a regression of a variable on its lagged value, an intercept, and a trend term. The distributions of both statistics depend on the coefficient of the trend, and the usual Dickey-Fuller tabulations assume that this coefficient equals zero. This paper provides tabulations for the case that the coefficient of the trend is non-zero.

A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test

Abstract: The panel data unit root test suggested by Levin and Lin (LL) has been widely used in several applications, notably in papers on tests of the purchasing power parity hypothesis. This test is based on a very restrictive hypothesis which is rarely ever of interest in practice. The Im–Pesaran–Shin (IPS) test relaxes the restrictive assumption of the LL test. This paper argues that although the IPS test has been offered as a generalization of the LL test, it is best viewed as a test for summarizing the evidence from a number of independent tests of the sample hypothesis. This problem has a long statistical history going back to R. A. Fisher. This paper suggests the Fisher test as a panel data unit root test, compares it with the LL and IPS tests, and the Bonferroni bounds test which is valid for correlated tests. Overall, the evidence points to the Fisher test with bootstrap-based critical values as the preferred choice. We also suggest the use of the Fisher test for testing stationarity as the null and also in testing for cointegration in panel data.

Variational Mode Decomposition

Abstract: During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.

Automatic Time Series Forecasting: The forecast Package for R

Abstract: Automatic forecasts of large numbers of univariate time series are often needed in business and other contexts. We describe two automatic forecasting algorithms that have been implemented in the forecast package for R. The first is based on innovations state space models that underly exponential smoothing methods. The second is a step-wise algorithm for forecasting with ARIMA models. The algorithms are applicable to both seasonal and non-seasonal data, and are compared and illustrated using four real time series. We also briefly describe some of the other functionality available in the forecast package.

Effects of Word-of-Mouth Versus Traditional Marketing: Findings from an Internet Social Networking Site

Abstract: The authors study the effect of word-of-mouth (WOM) marketing on member growth at an Internet social networking site and compare it with traditional marketing vehicles. Because social network sites record the electronic invitations from existing members, outbound WOM can be precisely tracked. Along with traditional marketing, WOM can then be linked to the number of new members subsequently joining the site (sign-ups). Because of the endogeneity among WOM, new sign-ups, and traditional marketing activity, the authors employ a vector autoregressive (VAR) modeling approach. Estimates from the VAR model show that WOM referrals have substantially longer carryover effects than traditional marketing actions and produce substantially higher response elasticities. Based on revenue from advertising impressions served to a new member, the monetary value of a WOM referral can be calculated; this yields an upper-bound estimate for the financial incentives the firm might offer to stimulate WOM.