Validating The Assumptions of Residuals in ARIMA Model for Daily Stock Price Data By using R

Identifying the past data and plannig for future is very important for every organization . Now a days Stock market playes a major role for the development of economy. For the countries economic development, stock market plays a vital role. For this modelling, forecasting is the best way to know the future stock prices based on the past stock prices data. In stock price data, forecasting of closed price plays a major role in financing economic decisions. The Arima model has developed and implemented in many applications .So the researchers utilize arima model in forecasting the closed prices of AMAZON stock price data for future which have been collected from AMAZON 2007-01-03, to 2020-10-12.In this paper the researcher aim is to forecast by using the ARIMA time series model with particular reference to Box and Jenkins approach on daily stock prices of AMAZON With open statistical software R. The validity of ARIMA model is tested by using the standard statistical tests. Keywords: Auto Regressive Integrated Moving Average, Auto Correlation Function, Partial Auto Correlation Function, Akaikae Information Criterion, Auto Regressive Conditional Heteroscedasticity

Comparing Two ARIMA Models for Daily Stock Price Data

Analyzing the past data and planning for future is very important for every public and private organizational decisions. Now a days individuals also using forecasting methods to invest in Stock market. Investments in mutual funds and in registered companies in companies in stock market is the order of the day. In this paper, advanced forecasting methods are fitted to the time related stock price data to study its effectiveness in forecasting future events. Auto correlation and standard models have been analyzed before fitting this model to the above data. The forecasting can be done by using the ARIMA time series(using auto. arima) model. A particular reference have been made to Box and Jenkins approach for day to day stock price data values of Exxon Mobile Corporation from '1995-01-01 to 2020-03-01. With usual statistical software R. Here, ARIMA(1,1,1,) is fitted to this data, These results are compared with the model ARIMA(1,1,1,) by using accuracy measures. Keywords: ARIMA: Auto Regressive Integrated Moving Average ACF: Auto Correlation Function PACF: Partial Auto Correlation Function AIC: Akaikae Information Criterion RMSE: Root mean square error XOM: Exxon Mobil Corporation

Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Specific Heat Capacity of Confined Water in Extremely Narrow Graphene Nanochannels

Specific heat capacity of extremely confined water determines its performance in the heat transfer as the sizes of devices decrease to nanoscales. Here, we report the basic data of the specific heat capacity of water confined in narrow graphene nanochannels below 5 nm in height using molecular dynamics simulations. The results show that the specific heat capacity of confined water is size-dependent, and the commensurability effect of the specific heat capacity presents as the confinement decreases to 1.7 nm. The deviation of specific heat capacity of confined water with that of bulk water is attributed to the variation of configuration features, including density distribution and hydrogen bonds, and vibration features, including velocity auto-correlation function and vibrational density of states. This work unveils the confinement effects and their physical mechanisms of the specific heat capacity of nanoconfined water, and the data provided here have wide prospects for energy applications at nanoscales.

Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences

This paper discusses the auto-correlation functions of m-bit random numbers obtained from m chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an m-bit sequence obtained by m binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the m-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated m-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate m-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated m-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to 1/2) and independent of one another.

Forecasting of Market Clearing Volume Using Wavelet Packet-Based Neural Networks with Tracking Signals

In order to analyze the nature of electrical demand series in deregulated electricity markets, various forecasting tools have been used. All these forecasting models have been developed to improve the accuracy of the reliability of the model. Therefore, a Wavelet Packet Decomposition (WPD) was implemented to decompose the demand series into subseries. Each subseries has been forecasted individually with the help of the features of that series, and features were chosen on the basis of mutual correlation among all-time lags using an Auto Correlation Function (ACF). Thus, in this context, a new hybrid WPD-based Linear Neural Network with Tapped Delay (LNNTD) model, with a cyclic one-month moving window for a one-year market clearing volume (MCV) forecasting has been proposed. The proposed model has been effectively implemented in two years (2015–2016) and unconstrained MCV data collected from the Indian Energy Exchange (IEX) for 12 grid regions of India. The results presented by the proposed models are better in terms of accuracy, with a yearly average MAPE of 0.201%, MAE of 9.056 MWh, and coefficient of regression (R2) of 0.9996. Further, forecasts of the proposed model have been validated using tracking signals (TS’s) in which the values of TS’s lie within a balanced limit between −492 to 6.83, and universality of the model has been carried out effectively using multiple steps-ahead forecasting up to the sixth step. It has been found out that hybrid models are powerful forecasting tools for demand forecasting.

Generalized Relational Tensors For Irregularly Sampled Time Series: Methods To Store, Re-generate, And Predict

The paper deals with a generalized relational tensor, a novel discrete structure to store information about a time series, and algorithms (1) to fill the structure, (2) to generate a time series from the structure, and (3) to predict a time series, for both regularly and irregularly sampled time series. The algorithms combine the concept of generalized z-vectors with ant colony optimization techniques. In order to estimate quality of the storing/re-generating procedure, a difference between characteristics of the initial and regenerated time series is used. The structure allows working with a multivariate time series, with an irregularly sampled time series, and with a number of series as well. For chaotic time series, a difference between characteristics of the initial time series (the highest Lyapunov exponent, the auto-correlation function) and those of the time series re-generated from a structure is used to assess the effectiveness of the algorithms in question. The approach has shown fairly good results for periodic and benchmark chaotic time series and satisfactory results for real-world chaotic data.

Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties

We construct generalized coherent states for the rationally extended Scarf-I potential. Statistical and geometrical properties of these states are investigated. Special emphasis is given to the study of spatio-temporal properties of the coherent states via the quantum carpet structure and the auto-correlation function. Through this study, we aim to find the signature of the “rationalization” of the conventional potentials and the classical orthogonal polynomials.

Application of Deep Learning Method for Daily Streamflow Time-Series Prediction: A Case Study of the Kowmung River at Cedar Ford, Australia

Sustainable management of water supplies faces a comprehensive challenge due to global climate change. Improving forecasts of streamflow based on erratic precipitation is a significant activity nowadays. In recent years, the techniques of data-driven have been widely used in the hydrological parameter’s prediction especially streamflow. In the current research, a deep learning model namely Long Short-Term Memory (LSTM), and two conventional machine learning models namely, Random Forest (RF), and Tree Boost (TB) were used to predict the streamflow of the Kowmung river at Cedar Ford in Australia. Different scenarios proposed to determine the optimal combination of input predictor variables, and the input predictor variables were selected based on the auto-correlation function (ACF). Model output was evaluated using indices of the root mean square error (RMSE), and the Nash and Sutcliffe coefficient (NSE). The findings showed that the LSTM model outperformed RF and TB in predicting the streamflow with RMSE and NSE equal to 102.411, and 0.911 respectively. for the LSTM model. The proposed model could adopt by hydrologists to solve the problems associated with forecasting daily streamflow with high precision. This study may not be generalized because of the geographical condition and the nature of the data for each location.