More generally, weighted averages may also be used. Moving averages are also called running means or rolling averages. They are a special case of “filtering”, which is a general process that takes one time series and transforms it into another time series. The term “moving average” is used to describe this procedure because each average is computed by dropping the oldest observation and includi...

Most scientific contributions addressing cybersecurity issues in water distribution networks (WDNs) propose detection systems without considering the location problem. A methodology for and of cyberattacks WDNs is proposed this paper. Structural analysis neural are effectively combined with control chart adaptive exponential weighted moving average (AEWMA). The framework requires only data from...

This study compares the forecasting performance of various Autoregressive integrated moving average (ARIMA) models by using time series data. Primarily, The Box-Jenkins approach is considered here for forecasting. For empirical analysis, we used CPI as a proxy for inflation and employed quarterly data from 1970 to 2006 for Pakistan. The study classified two important models for forecasting out ...

We show that the moving average process Xf (t) := ∫ t 0 f(t − s) dZ(s) t ∈ [0, T ] has a bounded version almost surely, when the kernel f has finite total 2– variation and Z is a symmetric Lévy process. We also obtain bounds for E| supt∈[0,T ] Xf (t)| and for uniform moduli of continuity of Xf ( · ) and for the largest jump of Xf ( · ) when it is not continuous. Similar results are obtained for...

We propose two new algorithms to go from any state-space model to an output equivalent and invertible Vector AutoRegressive Moving Average model with eXogenous regressors (VARMAX). As the literature shows how to do the inverse transformation, these results imply that both representations, statespace and VARMAX, are equally general and freely interchangeable. These algorithms are useful to solve...

We discuss computational aspects of likelihood-based estimation of univariate ARFIMA(p, d, q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.

This paper analyzes the second order bias of instrumental variables estimators for a dynamic panel model with fixed effects. Three different methods of second order bias correction are considered. Simulation experiments show that these methods perform well if the model does not have a root near unity but break down near the unit circle. To remedy the problem near the unit root a weak instrument...

In recent years many tools and algorithms for model comparison and differencing were proposed. Typically, the main focus of the research laid on being able to compute the difference in the first place. Only very few papers addressed the quality of the delivered differences sufficiently. Hence, this is a general shortcoming in the state-of-the-art. Currently, there are no established community s...

Penalized splines are widespread tools for the estimation of trend and cycle, since they allow a data driven estimation of the penalization parameter by the incorporation into a linear mixed model. Based on the equivalence of penalized splines and the Hodrick-Prescott filter, this paper connects the mixed model framework of penalized splines to the WienerKolmogorov filter. In the case that tren...