Hypothesis Testing in Time Series Analysis.

By P. Moran, P. Whittle. 1951

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Citations in the corpus

Long memory time series (2003, methodology): “The liter- ature on the Gaussian MLE developed first with short memory processes in mind (see e.g. Whittle, 1951, Hannan, 1973), and it may be helpful to provide some background to this.”
Hawkes and INAR($\infty$) processes (2015, background): “main result of the paper. To start with, we outline the history of the concepts involved. Standard time series theory for sequences of real-valued data points has been developed in seminal works like Whittle (1951) and Box and Jenkins (1970). This theory led to the natural question of time series mo”
Narrow-Band Analysis of Nonstationary Processes (2001, background): “For univariate time series, Gaussian rules of inference lead to consideration of quadratic forms, and Gaussian methods developed by Whittle (1951) and others in stationary short-range dependent environments were extended to unit root nonstationary ones by Box and Jenkins (1971), with limit theory de”
From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting (2020, methodology): “Several classic techniques such as Autoregressive Moving Average Models (ARMA) [43] have been incorporated in deep learning architectures [41, 16] in modern day state-of-theart time series forecasting methods [37].”
Forecasting Currency Volatility: A Comparison of Implied Volatilities and AR(FI)MA Models (2004, methodology): “The parameters of an ARFIMA(p, d, q) model4 can be estimated efficiently by maximizing the likelihood function.5 Whittle (1951) derived the log-likelihood function in the frequency domain for a Gaussian process, here calculated from T observations as ∑ +−= − = 1 1 )(/)(ˆ))(2ln( 2 1 T j jjj fffK…”
Detection of Multiple Structural Breaks in Multivariate Time Series (2013, methodology): “in the context of stationary processes [see Whittle (1951)].”
Modelling structural breaks, long memory and stock market volatility: an overview (2005, methodology): “Procedures for approximation of the log-likelihood have been proposed both in the frequency domain (Whittle, 1951; Fox and Taqqu, 1986; Beran, 1994a; Taqqu et al., 1995) or in the time domain, such as Haslett and Raftery (1989).”
Parameter estimates for fractional autoregressive spatial processes (2005, unknown): “d denote X= (X 11,X 12,...,XNN)∼N(0,ΓN). Let Logxdenote the natural logarithm of x. Then the log-likelihood function of X is LN(θ,σ2)=− N2 2 Log2π− 1 2 Log|ΓN|− 1 2 X′Γ−1 N X. Let VN = σ−2ΓN. Whittle [23] proves that |VN(θ)| → 1 as N→ ∞ and, thus, LN(θ,σ2) can be approximated by −N 2 2 Log2πσ 2 − 1 ”
Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration (2005, methodology): “An alternative approximate MLE of the ARFIMA(p, d, q) model follows the idea of Whittle (1951), who noted that for stationary models the covariance matrix Ω can be diagonalized by transforming the model into the frequency domain.”