Mathematics makes me wonder

This paper draws a picture of Mathematics education in the Philippines for Years 1 to 10. The factors included for this endeavor are the curriculum, the results of various national exams and the results of the studies undertaken by the International Association for the Evaluation of Educational Achievement

On the existence of calendar anomalies and persistence in the daily returns of the PSEi

The future of the stock market may never be predicted consistently, nor its past behavior understood entirely, but any knowledge gained from observing it could help decide on a sound investment strategy. In this study, I looked at the daily returns of the Philippine Stock Exchange index (PSEi) from March 1, 1990, to January 31, 2017, and see how the data relates to the mathematically verifiable aspects of the noise theory and efficient market theory (EMT). In relation to the noise theory, I looked at the occurrences of anomalies. For the EMT, I made use of discrete-time Markov chains to determine some trends. The study results showed that most stock market anomalies are present while persistent behavior is hardly present in the dataset. Furthermore, I applied day ahead time domain forecasting methods starting with the simple moving average models to autoregressive moving average models. The augmented Dickey-Fuller test indicate that the daily returns are a stationary series although the ACF and PACF plots have consistently shown non-zero correlations for lags 1, 9, 12, 13. I have obtained AR(1) and ARMA(1,2) processes for the data and both models indicate the same forecasting accuracy via the Diebold-Mariano test. Although these time domain processes were unable to predict the random noise in the data, these processes were accurate in predicting the signs of the values as supported by the Pesaran-Timmermann test. © 2018 by De La Salle University

Long-range dependence of stationary processes in single-server queues

The stationary processes of waiting times {W n }n = 1,2,... in a GI/G/1 queue and queue sizes at successive departure epochs {Q n}n = 1,2,... in an M/G/1 queue are long-range dependent when 3 \u3c κ S \u3c 4, where κ S is the moment index of the independent identically distributed (i.i.d.) sequence of service times. When the tail of the service time is regularly varying at infinity the stationary long-range dependent process {W n } has Hurst index 1/2(5-κ S ), i.e. sup {h : lim sup n→∞\, var(W1+⋯+Wn)/n 2h = ∞} = 5 - κS}/2 If this assumption does not hold but the sequence of serial correlation coefficients {ρ n } of the stationary process {W n } behaves asymptotically as cn -α for some finite positive c and α ∈ (0,1), where α = κ S - 3, then {W n } has Hurst index 1/2(5-κ S ). If this condition also holds for the sequence of serial correlation coefficients {r n } of the stationary process {Q n } then it also has Hurst index 1/2(5κ S ). © Springer Science+Business Media, LLC 2007

Forecasting day-ahead electricity prices of Singapore through ARIMA and wavelet-ARIMA

The changes observed in the electricity markets over the past decade brought about developments in the field of electricity modeling. In this paper, traditional AutoRegressive Integrated Moving Average (ARIMA) models and Wavelet-ARIMA models arc applied to the Singapore electricity market, Asia\u27s first liberalized electricity market. Forecasting will be done for each electricity price modelling technique and the adequacy of the models is tested through forecast accuracy. The comparison of forecast accuracy of the models is done across different data behaviors. Copyright © 2012 De La Salle University, Philippines