Large Sample Properties of Estimation in Time Series Observed at Unequally Spaced Times

1984 ◽  
pp. 58-77 ◽  
Author(s):  
W. Dunsmuir
Keyword(s):  
Time Series ◽  
Large Sample ◽  
Unequally Spaced

LamaH: Large-sample Data for Hydrology in Central Europe

2021 ◽  
Author(s):  
Christoph Klingler ◽  
Mathew Herrnegger ◽  
Frederik Kratzert ◽  
Karsten Schulz
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Vegetation Indices ◽  
River Network ◽  
Series Data ◽  
High Temporal Resolution ◽  
Stream Length ◽  
Discharge Data ◽  
Large Sample ◽  
Access To Data

<p>Open large-sample datasets are important for various reasons: i) they enable large-sample analyses, ii) they democratize access to data, iii) they enable large-sample comparative studies and foster reproducibility, and iv) they are a key driver for recent developments of machine-learning based modelling approaches.</p><p>Recently, various large-sample datasets have been released (e.g. different country-specific CAMELS datasets), however, all of them contain only data of individual catchments distributed across entire countries and not connected river networks.</p><p>Here, we present LamaH, a new dataset covering all of Austria and the foreign upstream areas of the Danube, spanning a total of 170.000 km² in 9 different countries with discharge observations for 882 gauges. The dataset also includes 15 different meteorological time series, derived from ERA5-Land, for two different basin delineations: First, corresponding to the entire upstream area of a particular gauge, and second, corresponding only to the area between a particular gauge and its upstream gauges. The time series data for both, meteorological and discharge data, is included in hourly and daily resolution and covers a period of over 35 years (with some exceptions in discharge data for a couple of gauges).</p><p>Sticking closely to the CAMELS datasets, LamaH also contains more than 60 catchment attributes, derived for both types of basin delineations. The attributes include climatic, hydrological and vegetation indices, land cover information, as well as soil, geological and topographical properties. Additionally, the runoff gauges are classified by over 20 different attributes, including information about human impact and indicators for data quality and completeness. Lastly, LamaH also contains attributes for the river network itself, like gauge topology, stream length and the slope between two sequential gauges.</p><p>Given the scope of LamaH, we hope that this dataset will serve as a solid database for further investigations in various tasks of hydrology. The extent of data combined with the interconnected river network and the high temporal resolution of the time series might reveal deeper insights into water transfer and storage with appropriate methods of modelling.</p>

scholarly journals Discrete-time autoregressive model for unequally spaced time-series observations

2019 ◽  
Vol 627 ◽  
pp. A120 ◽  
Author(s):  
Felipe Elorrieta ◽  
Susana Eyheramendy ◽  
Wilfredo Palma
Keyword(s):  
Time Series ◽  
State Space ◽  
Discrete Time ◽  
Likelihood Estimation ◽  
Variable Stars ◽  
Space Representation ◽  
Finite Sample ◽  
Unequally Spaced ◽  
Astronomical Time ◽  
Astronomical Time Series

Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuous-time autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discrete-time process. We show that the model is weakly stationary and that it can be represented as a state-space system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.

COGARCH Models

2020 ◽  
pp. 79-97
Author(s):  
Yakup Arı
Keyword(s):  
Differential Equation ◽  
Time Series ◽  
Continuous Time ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Unequally Spaced ◽  
Parameter Estimation Methods ◽  
Pseudo Maximum Likelihood ◽  
Gamma Processes ◽  
Methods Of Moments

In this chapter, the features of a continuous time GARCH (COGARCH) process is discussed since the process can be applied as an explicit solution for the stochastic differential equation which is defined for the volatility of unequally spaced time series. COGARCH process driven by a Lévy process is an analogue of discrete time GARCH process and is further generalized to solutions of Lévy driven stochastic differential equations. The Compound Poisson and Variance Gamma processes are defined and used to derive the increments for the COGARCH process. Although there are various parameter estimation methods introduced for COGARCH, this study is focused on two methods which are Pseudo Maximum Likelihood Method and General Methods of Moments. Furthermore, an example is given to illustrate the findings.

scholarly journals Brief communication "Improving the actual coverage of subsampling confidence intervals in atmospheric time series analysis"

2012 ◽  
Vol 19 (5) ◽  
pp. 473-477
Author(s):  
A. Gluhovsky ◽  
T. Nielsen
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Resampling Methods ◽  
Large Sample ◽  
Series Analysis

Abstract. In atmospheric time series analysis, where only one record is typically available, subsampling (which works under the weakest assumptions among resampling methods), is especially useful. In particular, it yields large-sample confidence intervals of asymptotically correct coverage probability. Atmospheric records, however, are often not long enough, causing a substandard coverage of subsampling confidence intervals. In the paper, the subsampling methodology is extended to become more applicable in such practically important cases.

scholarly journals Large-sample approximations for variance-covariance matrices of high-dimensional time series

Bernoulli ◽  
2017 ◽  
Vol 23 (4A) ◽  
pp. 2299-2329 ◽  
Author(s):  
Ansgar Steland ◽  
Rainer von Sachs
Keyword(s):  
Time Series ◽  
Covariance Matrices ◽  
High Dimensional ◽  
Large Sample

scholarly journals Determination of time-varying periodicities in unequally spaced time series of OH* temperatures using a moving Lomb–Scargle periodogram and a fast calculation of the false alarm probabilities

2020 ◽  
Vol 13 (2) ◽  
pp. 467-477 ◽  
Author(s):  
Christoph Kalicinsky ◽  
Robert Reisch ◽  
Peter Knieling ◽  
Ralf Koppmann
Keyword(s):  
Time Series ◽  
False Alarm ◽  
False Alarm Probability ◽  
Time Interval ◽  
Time Resolved ◽  
Fast Calculation ◽  
Unequally Spaced ◽  
Data Gaps ◽  
Analyse Time

Abstract. We present an approach to analyse time series with unequal spacing. The approach enables the identification of significant periodic fluctuations and the derivation of time-resolved periods and amplitudes of these fluctuations. It is based on the classical Lomb–Scargle periodogram (LSP), a method that can handle unequally spaced time series. Here, we additionally use the idea of a moving window. The significance of the results is analysed with the typically used false alarm probability (FAP). We derived the dependencies of the FAP levels on different parameters that either can be changed manually (length of the analysed time interval, frequency range) or that change naturally (number of data gaps). By means of these dependencies, we found a fast and easy way to calculate FAP levels for different configurations of these parameters without the need for a large number of simulations. The general performance of the approach is tested with different artificially generated time series and the results are very promising. Finally, we present results for nightly mean OH* temperatures that have been observed from Wuppertal (51∘ N, 7∘ E; Germany).

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