Triangle Momentum

<p>This research investigates the breakout of security prices from periods of sideways drift known as Triangles. Contributions are made to the existing literature by considering returns conditionally based on Triangles in particular terms of how momentum traders time positions, and by then using alternative statistical methods to more clearly show results. Returns are constructed by scanning for Triangle events, and determining simulated trader returns from predetermined price levels. These are compared with a Naive model consisting of randomly sampled events of comparable measure. Modelling of momentum results is achieved using a marked point Poisson process based approach, used to compare arrival times and profit/losses. These results are confirmed using a set of 10 day return heuristics using bootstrapping to define confidence intervals. Using these methods applied to CRSP US equity data inclusive from years 1960 to 2017, US equities show a consistent but weak predictable return contribution after Triangle events occur; however, the effect has decreased over time, presumably as the market becomes more efficient. While these observed short term momentum changes in price have likely been compensated to a degree by risk, they do show that such patterns have contained forecastable information about US equities. This shows that prices have likely weakly been affected by past prices, but that currently the effect has reduced to the point that it is of negligible size as of 2017.</p>

Triangle Momentum

<p>This research investigates the breakout of security prices from periods of sideways drift known as Triangles. Contributions are made to the existing literature by considering returns conditionally based on Triangles in particular terms of how momentum traders time positions, and by then using alternative statistical methods to more clearly show results. Returns are constructed by scanning for Triangle events, and determining simulated trader returns from predetermined price levels. These are compared with a Naive model consisting of randomly sampled events of comparable measure. Modelling of momentum results is achieved using a marked point Poisson process based approach, used to compare arrival times and profit/losses. These results are confirmed using a set of 10 day return heuristics using bootstrapping to define confidence intervals. Using these methods applied to CRSP US equity data inclusive from years 1960 to 2017, US equities show a consistent but weak predictable return contribution after Triangle events occur; however, the effect has decreased over time, presumably as the market becomes more efficient. While these observed short term momentum changes in price have likely been compensated to a degree by risk, they do show that such patterns have contained forecastable information about US equities. This shows that prices have likely weakly been affected by past prices, but that currently the effect has reduced to the point that it is of negligible size as of 2017.</p>

A Markov chain model for daily rainfall occurrences at east Thanjavur district

The occurrences and non-occurrences of the rainfall can be described by a two-state Markov chain. A dry date is denoted by state 0 and wet date is denoted by state 1. We have taken the sample which follows a Poisson process with known parameter. Using this Poisson sample we have given a new approach to affect statistical inference for the law of the Markov chain and state estimation concerning un-observed past values or not yet observed future values. The paper aims at comparing the earlier fit of the data with the new approach.

A Spatial Nonhomogeneous Poisson Process Model Using Bayesian Approach on a Space-Time Geostatistical Data

In this research, we propose the nonhomogeneous Poisson process on geostatistical data by adding a time component to be applied in the study case of air pollution in the Special Region of Yogyakarta. We use the Bayesian approach to inference the model using the MCMC method. And to generate samples of the posterior distribution, we wield the Metropolis-Hastings algorithm, and we obtained it has good convergence for this case. And to show the goodness of fit of this model, we had the value of DIC.

Poisson distribution and process as a well-fitting pattern for counting variables in biologic models

One of the major criticisms directed to basic research on high dilution effects is the lack of a steady statistical approach; therefore, it seems crucial to fix some milestones in statistical analysis of this kind of experimentation. Since plant research in homeopathy has been recently developed and one of the mostly used models is based on in vitro seed germination, here we propose a statistical approach focused on the Poisson distribution, that satisfactorily fits the number of non-germinated seeds. Poisson distribution is a discrete-valued model often used in statistics when representing the number X of specific events (telephone calls, industrial machine failures, genetic mutations etc.) that occur in a fixed period of time, supposing that instant probability of occurrence of such events is constant. If we denote with λ the average number of events that occur within the fixed period, the probability of observing exactly k events is: P(k) = e-λ λk /k! , k = 0, 1,2,… This distribution is commonly used when dealing with rare effects, in the sense that it has to be almost impossible to have two events at the same time. Poisson distribution is the basic model of the socalled Poisson process, which is a counting process N(t), where t is a time parameter, having these properties: - The process starts with zero: N(0) = 0; - The increments are independent; - The number of events that occur in a period of time d(t) follows a Poisson distribution with parameter proportional to d(t); - The waiting time, i.e. the time between an event and another one, follows and exponential distribution. In a series of experiments performed by our research group ([1], [2]., [3], [4]) we tried to apply this distribution to the number X of non-germinated seeds out of a fixed number N* of seeds in a Petri dish (usually N* = 33 or N* = 36). The goodness-of-fit was checked by different tests (Kolmogorov distance and chi-squared), as well as with the Poissonness plot proposed by Hoaglin [5]. The goodness-of-fit of Poisson distribution allows to use specific tests, like the global Poisson test (based on a chi-squared statistics) and the comparison of two Poisson parameters, based on the statistic z = X1–X2 / (X1+X2)1/2 which is, for large samples (at least 20 observations) approximately standard normally distributed. A very clear review of these tests based on Poisson distribution is given in [6]. This good fit of Poisson distribution suggests that the whole process of germination of wheat seeds may be considered as a non-homogeneous Poisson process, where the germination rate is not constant but changes over time. Keywords: Poisson process, counting variable, goodness-of-fit, wheat germination References [1] L.Betti, M.Brizzi, D.Nani, M.Peruzzi. A pilot statistical study with homeopathic potencies of Arsenicum Album in wheat germination as a simple model. British Homeopathic Journal; 83: 195-201. [2] M.Brizzi, L.Betti (1999), Using statistics for evaluating the effectiveness of homeopathy. Analysis of a large collection of data from simple plant models. III Congresso Nazionale della SIB (SocietàItaliana di Biometria) di Roma, Abstract Book, 74-76. [3] M.Brizzi, D.Nani, L.Betti, M.Peruzzi. Statistical analysis of the effect of high dilutions of Arsenic in a large dataset from a wheat germination model. British Homeopathic Journal, 2000;, 89, 63-67. [4] M.Brizzi, L.Betti (2010), Statistical tools for alternative research in plant experiments. “Metodološki Zvezki – Advances in Methodology and Statistics”, 7, 59-71. [5] D.C.Hoaglin (1980), A Poissonness plot. “The American Statistician”, 34, 146-149. [6] L.Sachs (1984) Applied statistics. A handbook of techniques. Springer Verlag, 186-189.