Properties of (Co)Sine Clock beyond the Unit Circle Definition
L. Franklin Kemp
(Co)Sine Clock Company, Plano Texas.
Abstract: (Co)Sine Clock is a unit circle clock that tells time and trigonometry. Study of the movement of cosine and sine hands reveals their derivatives, uniform circular motion, and simple harmonic motion. Low order polynomial interpolations lead to their power series expressions which appear to defy periodicity.
Pages: 235 – 238 | Full PDF Paper
Asymptotic Frequencies of Bounded Differential Equations
LSTA, University Pierre et Marie Curie Sorbonne, France.
Abstract: We study an ordinary differential equation as an iteration with a constant fixed path when the number of iterations goes to infinite. In such conditions, very different from these of classical analysis, we greatly increase the spectrum of the solutions. First, we treat this iteration in a probabilistic framework. Curves where the probability of presence is invariant are shown. There are also critical frequencies but their interpretation remains difficult.
Keywords: Invariant measures, Perron-Frobénius, function of Plancherel – Rotach, steepest descent’s method, Lorenz’s attractor, critical frequencies.
Pages: 239 – 255 | Full PDF Paper
Household Investment Forecast in The Stock Exchange of Thailand
Gorn Tepvorachai, Somsajee Siksamat, Yuwawan Rattakul Boonyaleephan
The Bank of Thailand, Bangkok, Thailand.
Abstract: The investment outlook of households is an important factor for domestic investment, leading to the expansion of domestic economy and possibly resulting in the improvement of household well-being. Therefore, the investment perspective of households can be used as an indicator of consumer confidence in the domestic economic outlook. This study creates a measure that reflects the household investment view through the actual investment in the Stock Exchange of Thailand (SET), forecasted one month ahead. The one month ahead security-by-security net household transaction is forecasted based on the Stock Exchange of Thailand’s internal security-by-security factors: stock price, stock trading volume, outstanding value by investors’ portfolio, price change effect by investors’ portfolio, and unit change effect (net transaction) by investors’ portfolio. The data used in this study is from secondary data source, collected monthly from January 2009 to July 2016 total of 91 months from the SET and the authors’ calculation. The net household transaction forecast is modelled by two comparison techniques: moving multiple regression (MMR) and moving artificial neural network (MANN). This study finds that MANN forecast produces lesser mean absolute error (MAE), root mean square error (RMSE), and mean absolute percent error (MAPE) statistics than the MMR, but higher directional accuracy (DA test) statistic than the MMR. Both MANN and MMR techniques produces significantly different forecasts with Diebold Mariano (MA test) statistic at 95% confidence level. This finding confirms the MANN forecast is more efficient and more accurate than the MMR forecast. The MANN forecast suggests the household investment is positively affected by stock price and price change effect within household’s portfolio. On the other hand, the MANN forecast suggests the household investment is adversely affected by the outstanding portfolio value of the non-financial investors, financial investors, and public investors.
Keywords: Investment outlook, Unit change, Security-by-security, Moving artificial neural network.
Pages: 256 – 265 | Full PDF Paper