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Time Series Forecasting
Published in Harry G. Perros, An Introduction to IoT Analytics, 2021
Let Xt be a random variable indicating the value of a time series at time t. The autoregressive model predicts the next value Xt for time t using the expression:Xt=δ+a1Xt−1+a2Xt−2+…+apXt−p+εtwhere Xt−1, Xt−2, …, Xt−p are the random variables indicating the previous p observed values of the time series, δ is a constant, ai, i = 1, 2, …, p, are weights, and εt is normally distributed white noise with 0 mean and variance σ2. The autoregressive model is referred to as AR(p), where p is the order of the model. We note that the autoregressive model is a linear regression of the next value of the time series against one or more prior values of the time series.
Flood Forecasting
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Priyanka Sharma, Pravin Patil, Saeid Eslamian
The autoregressive model regresses against the past values of the time series. Mathematically, the autoregressive model can be expressed as (Box and Jenkins, 1976): zt=ε+∅1zt−1+…+∅pzt−p+at
Differential effects of public and private funding in the medical device industry
Published in Expert Review of Medical Devices, 2018
Employment serves as the common economic output production for both VC and NIH funding inputs. We investigate the period of 5 years after VC and NIH funding are endowed in the regions. We control for the level of employment in the previous year (t − 1) of the endowments of VC and NIH funding (t) and MSA and year-fixed effects, resulting in our empirical specification being a first-order autoregressive model, AR(1) with fixed effects. The autoregressive model is a common approach to describe time-varying processes and specifies that the output variable depends linearly on its own previous values. Specifically, we used the following econometrics model to predict the level of employment () as
ARIMA forecasting of China’s coal consumption, price and investment by 2030
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2018
Shumin Jiang, Chen Yang, Jingtao Guo, Zhanwen Ding
The ARIMA model is the most common time-series model in the forecasting analysis. ARIMA forecasting analysis mainly consists of two basic parts, AR(p) and MA(q). The AR(p) model refers to the autoregressive model of order p. The MA(q) model refers to the moving average model of order q. An ARMA(p,q) model of order p and q is applied when data show evidence of nonstationarity and defined by
Establishment and application of a fractional difference-autoregressive model for daily runoff time series forecasting based on wavelet analysis
Published in Systems Science & Control Engineering, 2018
Jie Zhang, Meili Wang, JieLong Hu
If the time series is non-stationary, we cannot establish an autoregressive model with it. The first order difference is a frequently-used method, but it may lead to the over difference problem. Mills (2002) found the relationship between the difference order ‘d’ and the variance of the time series. The variance will decrease with the increase of the difference order until it becomes a stable time series, and then it is going to increase.