Yuichi Goto

Kyushu University | Kyudai

Time-reversibility is a crucial feature of many time series models, while time-irreversibility is the rule rather than the exception in real-life data. Testing the null hypothesis of time-reversibilty, therefore, should be an important step preliminary to the identification and estimation of most traditional time-series models. Existing procedures,...

In this chapter, we illustrate some numerical studies investigating the finite sample performance of the tests for one-way and two-way models presented in the previous chapters. First, we demonstrate the performance of the Lawley–Hotelling test statistic (LH), the likelihood ratio test statistic (LR), and the Bartlett–Nanda–Pillai test statistic (B...

The optimality of the tests has not been discussed so far. For the test for the existence of fixed effects, the locally asymptotically maximin test based on local asymptotic normality (LAN) was proposed by Hallin et al. (2021) for i.i.d. data. In this chapter, we show that the one-way random effect model for i.i.d. sequences does not have the LAN p...

While ANOVA for independent errors has been well-tuned, ANOVA for time-dependent errors is in its infancy. In this chapter, we extend the one-way fixed model with independent errors and groups to a one-way fixed model with time-dependent errors and independent groups.

This chapter extends the one-way models with time-dependent errors and correlated groups dealt with in Chapter 4 to the two-way models with time-dependent errors and correlated groups. We propose a test for the existence of random effects in Section 5.1 and a test for the existence of random interactions in Section 5.2. We show that the tests have...

The independence between groups was imposed in Chapter 2 but this assumption is not fulfilled by some real data, e.g., stock prices. This chapter extends one-way fixed models with time-dependent errors and independent groups dealt with in Chapter 2 to one-way fixed and random models with time-dependent errors and correlated groups. We propose a tes...

Although finite dimensionality was assumed in Chapter 2, ANOVA for high-dimensional time-dependent errors has not been fully developed. In this chapter, we extend the one-way fixed model with time-dependent errors and independent groups to a one-way fixed model with high-dimensional time-dependent errors and independent groups. In Section 3.1, we d...

This chapter analyzes the average wind speed data observed in seven cities located in coastal and inland areas in Japan by assuming the one-way effect model with time-dependent errors and correlated groups. The purpose is to assess the existence of area effects. To this end, both the \( T_{\textrm{GALT},n}\) statistic designed for correlated groups...

The integer autoregressive (INAR) model is one of the most commonly used models in nonnegative integer-valued time series analysis and is a counterpart to the traditional autoregressive model for continuous-valued time series. To guarantee the integer-valued nature, the binomial thinning operator or more generally the generalized Steutel and van Ha...

We investigate tests for a structural break for nonnegative integer-valued time series. This topic has been intensively studied in recent years. We deal with the model whose conditional expectation is endowed with dependence structures. Unknown parameters of the model are estimated by an M-estimator. Then, we study three types of test statistics: t...

Coherence is a widely used measure to assess linear relationships between time series. However, it fails to capture nonlinear dependencies. To overcome this limitation, this paper introduces the notion of residual spectral density as a higher-order extension of the squared coherence. The method is based on an orthogonal decomposition of time series...

We consider the sparse principal component analysis for high‐dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish oracle inequalities for penalized principal component estimators for the large class of processes including heavy‐tailed time series. The ra...

In this paper, we propose tests for the existence of random effects and interactions for two-way models with dependent errors. We prove that the proposed tests are asymptotically distribution-free which have asymptotically size \({{\tau }}\) and are consistent. We elucidate the nontrivial power under the local alternative when a sample size tends t...

We consider the problem of testing for the existence of fixed effects and random effects in one-way models, where the groups are correlated and the disturbances are dependent. The classical F-statistic in the analysis of variance is not asymptotically distribution-free in this setting. To overcome this problem, we propose a new test statistic for t...

В статье показывается свойство локальной асимптотической нормальности (LAN) для криволинейных нормальных семейств и систем одновременных уравнений. Кроме того, показано, что односторонние случайные модели ANOVA не имеют свойства локальной асимптотической нормальности. Рассматриваются два случая, когда дисперсия случайного эффекта лежит внутри и на...

Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the entire joint distributions and thus avoiding the limitations of classical, $L^2$-based spectral methods. Most of...

We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for penalized principal component estimators for the processes including heavy-tailed time series. The consistency o...

Binary time series can be derived from an underlying latent process. In this paper, we consider an ellipsoidal alpha mixing strictly stationary process and discuss the discriminant analysis and propose a classification method based on binary time series. Assume that the observations are generated by time series which belongs to one of two categorie...

Zero crossing (ZC) statistic is the number of zero crossings observed in a time series. The expected value of the ZC specifies the first‐order autocorrelation of the processes. Hence, we can estimate the autocorrelation by using the ZC estimator. The asymptotic consistency and normality of the ZC estimator for scalar Gaussian processes are already...