The Econometric Modelling of Financial Time Series

Mills, Terence C.; Markellos, Raphael N.

doi:10.1017/cbo9780511817380

Cited by 164 publications

(105 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Next, we study a stochastic first-order autoregressive model for environmental change: a so-called AR (1) process (Mills and Markellos 2008). Autoregressive processes are commonly used to model time series, for instance, patterns of climate change (Bloomfield and Nychka 1992;Hay et al 2002).…”

Section: Random Fluctuations In Selection Coefficientsmentioning

confidence: 99%

Establishment of New Mutations in Changing Environments

Peischl

Kirkpatrick

2012

Genetics

View full text Add to dashboard Cite

Understanding adaptation in changing environments is an important topic in evolutionary genetics, especially in the light of climatic and environmental change. In this work, we study one of the most fundamental aspects of the genetics of adaptation in changing environments: the establishment of new beneficial mutations. We use the framework of time-dependent branching processes to derive simple approximations for the establishment probability of new mutations assuming that temporal changes in the offspring distribution are small. This approach allows us to generalize Haldane's classic result for the fixation probability in a constant environment to arbitrary patterns of temporal change in selection coefficients. Under weak selection, the only aspect of temporal variation that enters the probability of establishment is a weighted average of selection coefficients. These weights quantify how much earlier generations contribute to determining the establishment probability compared to later generations. We apply our results to several biologically interesting cases such as selection coefficients that change in consistent, periodic, and random ways and to changing population sizes. Comparison with exact results shows that the approximation is very accurate.T HE process of adaptation depends on the establishment of new beneficial mutations. To be successful, it is not sufficient that mutations simply enter a population; they have to survive an initial phase of strong random genetic drift during which they can be lost. Once a beneficial mutation rises to a sufficiently large number of copies, the strength of drift becomes negligible and selection drives them to fixation or maintains them at intermediate frequency. The probability that mutations survive loss has been called the probability of fixation, the probability of establishment, or the probability of invasion, depending on the context. This probability plays an important role in determining the rate of adaptation of populations (Gillespie 2000;Orr 2000).Fixation probabilities of beneficial, neutral, or deleterious mutations have been at the core of population genetics theory since the early days of the field. Traditionally, two alternative frameworks have been used: branching processes (Fisher 1922) and diffusion approximations (Kimura 1962). Branching processes allow for the derivation of simple analytical results. Simulations show that these results are accurate, provided the population size is sufficiently large such that N s 1. The disadvantage of this approach is that it is limited to beneficial and initially rare mutations. Diffusion approximations on the other hand are more powerful and flexible. One can study deleterious or neutral mutations of arbitrary initial frequency. The downside is that it is often impossible to obtain simple analytical results and the underlying assumptions are often less intuitive than in branching processes.Using branching processes, Haldane (1927) derived his famous result that the probability of fixation of a benefici...

show abstract

Section: Random Fluctuations In Selection Coefficientsmentioning

confidence: 99%

Establishment of New Mutations in Changing Environments

Peischl

Kirkpatrick

2012

Genetics

View full text Add to dashboard Cite

show abstract

“…The characteristics of the sample variances associated with different orders of differencing can provide a useful means of deciding the appropriate order of differencing [19] cited also in Alamarew et al [3]. The sample variances will decrease until a stationary sequence has been found.…”

Section: Variance Comparisonsmentioning

confidence: 99%

“…This equation (19) can also be multiplied out and rewritten in a form that is used in forecasting as: …”

Section: Diagnostic Checkingmentioning

confidence: 99%

Prediction of Long-term Pattern and its Extreme Event Frequency of Rainfall in Dire Dawa Region, Eastern Ethiopia

Solomon¹

2015

J Climatol Weather Forecasting

View full text Add to dashboard Cite

Rainfall is the most critical and key variable both in atmospheric and hydrological cycle. Its patterns usually have spatial and temporal variability. Its variability is assumed to be the main cause for the frequently occurring climate extreme events such as drought and flood. In this study, spectrum analysis, cross-spectral analysis as well as seasonal auto-regressive integrated moving average (SARIMA) model were used in intending to predict the pattern and its extreme event frequency of rainfall in Dire Dawa Region based on data obtained from Dire Dawa and adjacent stations: Dengego and Haramaya. The result indicated that the amount of rainfall at Dengego and Haramaya are more or less the same on average in all seasons and much higher than that of Dire Dawa during last 30 year study period. The variability of annual rainfall in Dire Dawa during the study period is a bit larger than neighboring station's rainfall (Dengego and Haramaya), indicating that climate instability is high in Dire Dawa than other nearby stations. The result also indicates that relatively there is a tendency of increasing pattern in average annual rainfall of Dire Dawa in forecasted period. In the region, the rainfall extreme event like flood predicts or inferred to be recurring at about 4.17 years. Moreover, the rainfall periodicities of Dengego and Dire Dawa are found to be more likely associated, which implies that rainfall extreme event frequency in two districts is statistical significantly associated. It is proposed that assessing the factors that cause the fluctuation in the pattern and frequency of rainfall distribution in the region is needed to be study. The impacts of climate variability and climate change are evident on almost all socio-economic sectors. The output of this study can play an important role in the design of hydrological structures in the area of study and help the policy makers in improve their decisions by taking into consideration the available and future water resources. Prediction of Long-term Pattern and its Extreme Event Materials and Methods Data and variable of the studyA time series of monthly 30 years rainfall data in mm for the period January, 1984 to January, 2014 collected by the National Meteorological Agency of Ethiopia were used in the study. The data were collected from the synoptic stations of Dire Dawa and adjacent station: Dengego and Haramaya for further investigation. MethodologyThe development of climatology as a science has given rise to growing statistical applications on climatic information. Conducting investigations using standard statistical methodologies is an essential step in the development of climatology [13]. For instance, time series analysis is used in order to evaluate the temporal and spatial behavior of rainfall [14]. In this study a univariate Box-Jenkins Methods, in particular, Seasonal Autoregressive Integrated Moving Average (SARIMA) methods and spectral analysis and cross-spectral analysis are employed [15].Seasonal autoregressive integrated moving average (SA...

show abstract

“…Applications of these concepts to financial time series are provided by Campbell, Lo, and MacKinlay (1997), Mills (1999), Gourieroux and Jasiak (2001), Tsay (2001), Alexander (2001), andChan (2002). The problem we are having in this research is of quantifying each observation as the survey is being filled by each student such after each observation a value represents population with that particular option.…”

Section: Econometric Modelingmentioning

confidence: 99%

Autoregression and decision making under uncertainty

Shrivastava¹,

Prakash²,

Dhar³

et al. 2010

MAS

View full text Add to dashboard Cite

There are innumerable social and economic situations in which we are influenced in our decision making by what others are doing. Under uncertainty it's general tendency of an individual to get inspired by decisions of others or mass opinion. However, such herd behavior many times leads to autoregressive affect i.e. output at some moment is weighted average of past few observation. Hence can autoregressive models be used to predict the outcomes in the situations exhibiting such behavior? Studies have already been done on herd behavior in financial market. So, can models used to forecast financial markets be used to predict general decision making under uncertainty. To prove the validity of the point we conduct a small experiment of human decision making under uncertainty and try to forecast future responses using autoregressive models. A group of students were surveyed such that they can also look upon previous responses which would promote herding. A unique financial market type framework is used to quantify the responses and time series models of auto regression are used to forecast mass opinion.

show abstract

The Econometric Modelling of Financial Time Series

Cited by 164 publications

References 0 publications

Establishment of New Mutations in Changing Environments

Establishment of New Mutations in Changing Environments

Prediction of Long-term Pattern and its Extreme Event Frequency of Rainfall in Dire Dawa Region, Eastern Ethiopia

Autoregression and decision making under uncertainty

Contact Info

Product

Resources

About