This correspondence addresses the asymptotic normal distribution of the sample mean and the sample covariance matrix of mixed spectra time series containing a sum of sinusoids and a moving average (MA) process. Two central limit (CL) theorems are proved. As an application of this result, the asymptotic normal distribution of any sinusoidal frequencies estimator of such time series based on seco...

This review offers a guided tour to PcGive 10 modules for econometrics analysis of time series (PcGive), limited dependent variable (LogitJD) and static and dynamic panel data analyses (DPD), financial econometric (GARCH) and time series (ARFIMA) modelling. Several empirical applications are reported to illustrate the package.

Over time, Stata has come to incorporate more and more features for effective analysis of time series data, either pure time series or panel data with emphasis placed on the time series dimension of the panel. In this context, ‘time series modeling’ should be taken in the broad sense, referring to multivariate models built with data organized as time series, rather than the narrow sense of “Box...

Business cycle estimates are typically the output of a two-stage filtering process: a statistical agency first publishes seasonally adjusted data, and from this an econometrician estimates the cycle. In many cases the two filtering procedures used are not compatible, because two different agents are acting on the data independently. This paper derives formulas to state the signal extraction Mea...

In practice, signal extraction is based on finite samples X1, ..., XT and, very often, current estimates of the interesting components (t = T ) import: a socalled ‘concurrent’ or ‘real-time’ estimate of the trend or of its turning-points has a strong prospective content, since the future evolution of the time series is likely to be conditioned by this component. Whereas forecasting tools genera...

Real-world financial time series often contain both linear and nonlinear patterns. However, traditional time series analysis models, such as ARIMA, hold the assumption that a linear correlation exists among time series values while leaving nonlinear relation into error terms. Based on financial theories, we argue that investor sentiment is the main contributor to nonlinear pattern of stock time...

In many intervention analysis applications, time series data may be expensive or otherwise difficult to collect. In this case the power function is helpful, because it can be used to determine the probability that a proposed intervention analysis application will detect a meaningful change. Assuming that an underlying autoregressive integrated moving average (ARIMA) or fractional ARIMA model is...

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...