Long Memory Analysis of Daily Average Temperature Time Series

Theoretical and Applied Climatology, 2015

Enterprising endeavour has been taken in this work to realize and estimate the persistence in memory of the daily mean dew point time series obtained from seven different weather stations viz. Kolkata, Chennai (Madras), New Delhi, Mumbai (Bombay), Bhopal, Agartala and Ahmedabad representing different geographical zones in India. Hurst exponent values reveal an anti-persistent behaviour of these dew point series. To affirm the Hurst exponent values, five different scaling methods have been used and the corresponding results are compared to synthesize a finer and reliable conclusion out of it. The present analysis also bespeaks that the variation in daily mean dew point is governed by a non-stationary process with stationary increments. The delay vector variance (DVV) method has been exploited to investigate nonlinearity, and the present calculation confirms the presence of deterministic nonlinear profile in the daily mean dew point time series of the seven stations.

Long-memory is often observed in time series data. The existence of long-memory in a data set implies that the successive data points are strongly correlated i.e. they remain persistent for quite some time. A commonly used approach in modelling the time series data such as the Box and Jenkins models are no longer appropriate since the assumption of stationary is not satisfied. Thus, the scaling analysis is particularly suitable to be used for identifying the existence of long-memory as well as the extent of persistent data. In this study, an analysis was carried out on the observed daily mean per hour of ozone concentration that were available at six monitoring stations located in the urban areas of Peninsular Malaysia from 1998 to 2006. In order to investigate the existence of long-memory, a preliminary analysis was done based on plots of autocorrelation function (ACF) of the observed data. Scaling analysis involving five methods which included rescaled range, rescaled variance, dispersional, linear and bridge detrending techniques of scaled windowed variance were applied to estimate the hurst coefficient (H) at each station. The results revealed that the ACF plots indicated a slow decay as the number lag increased. Based on the scaling analysis, the estimated H values lay within 0.7 and 0.9, indicating the existence of long-memory in the ozone time series data. In addition, it was also found that the data were persistent for the period of up to 150 days. abSTraK Ingatan-panjang sering diperhatikan dalam data siri masa. Kewujudan ingatan-panjang dalam set data menunjukkan bahawa titik-titik data yang berturut adalah amat berkait rapat dan berterusan dalam suatu tempoh. Satu pendekatan yang biasa digunakan dalam pemodelan data siri masa seperti model Box dan Jenkins tidak lagi sesuai berikutan andaian kepegunan tidak dipenuhi. Oleh itu, analisis penskalaan sangat sesuai untuk digunakan bagi mengenal pasti kewujudan ingatan-panjang serta sifat keberterusan data. Dalam kajian ini, analisis dijalankan ke atas data cerapan purata harian per jam siri masa ozon yang diperoleh daripada enam stesen pemantauan yang terletak di kawasan Bandar di Semenanjung Malaysia dari tahun [1998][1999][2000][2001][2002][2003][2004][2005][2006]. Bagi tujuan penyiasatan kewujudan ingatan-panjang, analisis awal dilakukan berdasarkan kepada plot fungsi autokorelasi (ACF) bagi data yang dicerap. Analisis penskalaan yang terdiri daripada lima kaedah penskalaan yang berbeza yang merangkupi julat penskalaan semula, varians penskalaan semula, penyerakan, teknik penyahan tren linear dan jambatan dalam penskalaan varians tertingkap (SWV) digunakan untuk menganggar pekali hurst (H) bagi setiap stesen. Keputusan menunjukkan bahawa plot ACF siri data menyusut dengan lambat selaras peningkatan lag. Berdasarkan analisis penskalaan, purata anggaran H terletak di antara 0.7 dan 0.9 menunjukkan kewujudan memori-panjang dalam siri masa ozon. Selain itu, didapati bahawa data tersebut berterusan sehingga ke 150 hari.

Journal of Statistical Computation and Simulation, 2006

This paper discusses extensions of the popular methods proposed by Geweke and Porter-Hudak [Geweke, J. and Porter-Hudak, S., 1983, The estimation and application of long memory times series models.

This paper deals with the analysis of the temperatures in a group of 36 African countries. By looking at the maximum, minimum and the range (the difference between the maximum and the minimum) and using a long memory model based on fractional integration and cointegration, we first show that all series display a long memory pattern, with a significant positive time trend in 29 countries for the maximum temperatures and in 33 for the minimum ones. Looking at the range, the estimated value for the order of integration is smaller than the one based on maximum or minimum temperatures in 17 countries. Performing fractional cointegration tests between the maximum and minimum temperatures, our results indicate that the two series cointegrate in the classical sense (i.e., with a short memory equilibrium relationship) in a group of 11 countries, and there is another group of eight countries displaying cointegration in a fractional sense. The remaining 17 countries with no evidence of cointeg...

2018

This paper studies seasonal long-memory processes with Gegenbauer-type spectral densities. Estimates for singularity location and long-memory parameters based on general filter transforms are proposed. It is proved that the estimates are almost surely convergent to the true values of parameters. Solutions of the estimation equations are studied and adjusted statistics are proposed. Numerical results are presented to confirm the theoretical findings.

Hydrology and Earth System Sciences Discussions

A short memory process that encounters occasional structural breaks in mean can show a slower rate of decay in the autocorrelation function and other properties of fractional integrated I(d) processes. In this paper we employed a procedure for estimating the fractional differencing parameter in semi parametric contexts proposed by Geweke and Porter-Hudak to analyze nine daily rainfall data sets across Malaysia. The results indicate that all the data sets exhibit long memory. Furthermore, an empirical fluctuation process using the Ordinary Least Square (OLS) based cumulative sum (CUSUM) test with F-statistic for the break date were applied, break dates were detected in all data sets. The data sets were partitioned according to their respective break date and further test for long memory was applied for all subseries. Results show that all subseries follows the same pattern with the original series. The estimate of the fractional parameters d 1 and d 2 on the subseries obtained by splitting the original series at the break-date, confirms that there is a long memory in the DGP. Therefore this evidence shows a true long memory not due to structural break.

2008

The hedging of weather risks has become extremely relevant in recent years, promoting the diffusion of weather derivative contracts. The pricing of such contracts require the development of appropriate models for the prediction of the underlying weather variables. Within this framework, we present a modification of the double long memory ARFIMA-FIGARCH model introducing time-varying memory coefficients for both mean and variance. The model satisfies the empirical evidence of changing memory observed in average temperature series and provide useful improvements in the forecasting, simulation and pricing issues related to weather derivatives. We present an application related to the forecast and simulation of temperature indices used for pricing of weather options.

2019

Modells für realisierte Volatilitäten des S&P Index zu evaluieren. Wir kommen zu dem Ergebnis, dass sich Prognosen signifikant verbessern, wenn Sprünge im log-Preis-Prozess separat von kontinuierlichen Komponenten behandelt werden. Im Gegensatz dazu stellt sich heraus, dass Verbesserungen die durch die Inklusion von implizierter Volatilität erreicht werden insignifikant sind.

Physical Review E, 2011

The occurrence of persistence in climatic systems has been investigated by analyzing 1167 surface temperature records, covering 110 years, in the whole United States. Due to the nonlinear and nonstationary character of temperature time series, the seasonal cycle suffers from both phase and amplitude modulations, which are not properly removed by the classical definition of the temperature anomaly. In order to properly filter out the seasonal component and the monotonic trends, we define the temperature anomaly in a different way by using the empirical mode decomposition (EMD). The essence of this method is to empirically identify the intrinsic oscillatory modes from the temperature records according to their characteristic time scale. The original signal is thus decomposed into a collection of a finite small number of intrinsic mode functions (IMFs), having its own time scale and representing oscillations experiencing amplitude and phase modulations, and a residue, describing the mean trend. The sum of all the IMF components as well as the residue reconstructs the original signal. Partial reconstruction can be achieved by selectively choosing IMFs in order to remove trivial trends and noise. The EMD description in terms of time-dependent amplitude and phase functions overcomes one of the major limitation of the Fourier analysis, namely, a correct description of nonlinearities and nonstationarities. By using the EMD definition of temperature anomalies we found persistence of fluctuations with a different degree according to the geographical location, on time scales in the range 3-15 years. The spatial distribution of the detrended fluctuation analysis exponent, used to quantify the degree of memory, indicates that the long-term persistence could be related to to the presence of climatic regions, which are more sensitive to climatic phenomena such as the El Niño southern oscillation.

Mathematics and Computers in Simulation, 2011

In the literature many papers state that long-memory time series models such as Fractional Gaussian Noises (FGN) or Fractionally Integrated series (FI(d)) are empirically indistinguishable from models with a non-stationary mean, but which are mean reverting. We present an analysis of the statistical cost of model mis-specification when simulated long memory series are analysed by Atheoretical Regression Trees (ART), a structural break location method. We also analysed three real data sets, one of which is regarded as a standard example of the long memory type. We find that FGN and FI(d) processes do not account for many features of the real data. In particular, we find that the data sets are not H-self-similar. We believe the data sets are better characterized by non-stationary mean models.