Autoregressive — Indicators and Strategies

ARIMA Indicator with Optional Smoothing Overview The ARIMA (AutoRegressive Integrated Moving Average) Indicator is a powerful tool used to forecast future price movements by combining differencing, autoregressive, and moving average components. This indicator is designed to help traders identify trends and potential reversal points by analyzing the historical price data. Key Features AutoRegressive Component (AR): Utilizes past values to predict future prices. Moving Average Component (MA): Averages past price differences to smooth out noise. Differencing: Reduces non-stationarity in the time series data. Optional Smoothing: Applies EMA to the ARIMA output for a smoother signal. Customizable Parameters: Allows users to adjust AR and MA orders, differencing periods, and smoothing lengths. Concepts Underlying the Calculations Differencing: Subtracts previous prices from current prices to remove trends and seasonality, making the data stationary. AutoRegressive Component (AR): Predicts future prices based on a linear combination of past values. Moving Average Component (MA): Uses past forecast errors to refine future predictions. Exponential Moving Average (EMA): Applies more weight to recent prices, providing a smoother and more responsive signal. How It Works The ARIMA Indicator first calculates the differenced series to achieve stationarity. Then, it computes the simple moving average (SMA) of this differenced series. The indicator uses the AR and MA components to adjust the SMA, creating an approximation of the ARIMA model. Finally, an optional smoothing step using EMA can be applied to the ARIMA approximation to produce a smoother signal. How Traders Can Use It Traders can use the ARIMA Indicator to: Identify Trends: Detect emerging trends by observing the direction of the ARIMA line. Spot Reversals: Look for divergences between the ARIMA line and the price to identify potential reversal points. Generate Trading Signals: Use crossovers between the ARIMA line and the price to generate buy or sell signals. Filter Noise: Enable the optional smoothing to filter out market noise and focus on significant price movements. Example Usage Instructions Add the ARIMA Indicator to your chart. Adjust the input parameters to suit your trading strategy: Set the SMA Length (e.g., 14). Choose the Differencing Period (e.g., 1). Define the AR Order (p) and MA Order (q) (e.g., 1). Configure the Smoothing Length if smoothing is desired (e.g., 5). Enable or disable smoothing as needed. Observe the ARIMA line (blue) and compare it to the price chart. Use the ARIMA line to identify trends and potential reversals. Implement trading decisions based on the ARIMA line’s behavior relative to the price.

Itakura-Saito Autoregressive Extrapolation of Price [Loxx]Itakura-Saito Autoregressive Extrapolation of Price is an indicator that uses an autoregressive analysis to predict future prices. This is a linear technique that was originally derived or speech analysis algorithms. What is Itakura-Saito Autoregressive Analysis? The technique of linear prediction has been available for speech analysis since the late 1960s (Itakura & Saito, 1973a, 1970; Atal & Hanauer, 1971), although the basic principles were established long before this by Wiener (1947). Linear predictive coding, which is also known as autoregressive analysis, is a time-series algorithm that has applications in many fields other than speech analysis (see, e.g., Chatfield, 1989). Itakura and Saito developed a formulation for linear prediction analysis using a lattice form for the inverse filter. The Itakura–Saito distance (or Itakura–Saito divergence) is a measure of the difference between an original spectrum and an approximation of that spectrum. Although it is not a perceptual measure it is intended to reflect perceptual (dis)similarity. It was proposed by Fumitada Itakura and Shuzo Saito in the 1960s while they were with NTT. The distance is defined as: The Itakura–Saito distance is a Bregman divergence, but is not a true metric since it is not symmetric and it does not fulfil triangle inequality. read more: Selected Methods for Improving Synthesis Speech Quality Using Linear Predictive Coding: System Description, Coefficient Smoothing and Streak Data inputs Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar LastBar - bar where to start the prediction PastBars - how many bars back to model LPOrder - order of linear prediction model; 0 to 1 FutBars - how many bars you want to forward predict Things to know Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages. This indicator repaints Related Indicators (linear extrapolation of price) Levinson-Durbin Autocorrelation Extrapolation of Price Weighted Burg AR Spectral Estimate Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price

Helme-Nikias Weighted Burg AR-SE Extra. of Price [Loxx]Helme-Nikias Weighted Burg AR-SE Extra. of Price is an indicator that uses an autoregressive spectral estimation called the Weighted Burg Algorithm, but unlike the usual WB algo, this one uses Helme-Nikias weighting. This method is commonly used in speech modeling and speech prediction engines. This is a linear method of forecasting data. You'll notice that this method uses a different weighting calculation vs Weighted Burg method. This new weighting is the following: w = math.pow(array.get(x, i - 1), 2), the squared lag of the source parameter and w += math.pow(array.get(x, i), 2), the sum of the squared source parameter This take place of the rectangular, hamming and parabolic weighting used in the Weighted Burg method Also, this method includes Levinson–Durbin algorithm. as was already discussed previously in the following indicator: Levinson-Durbin Autocorrelation Extrapolation of Price What is Helme-Nikias Weighted Burg Autoregressive Spectral Estimate Extrapolation of price? In this paper a new stable modification of the weighted Burg technique for autoregressive (AR) spectral estimation is introduced based on data-adaptive weights that are proportional to the common power of the forward and backward AR process realizations. It is shown that AR spectra of short length sinusoidal signals generated by the new approach do not exhibit phase dependence or line-splitting. Further, it is demonstrated that improvements in resolution may be so obtained relative to other weighted Burg algorithms. The method suggested here is shown to resolve two closely-spaced peaks of dynamic range 24 dB whereas the modified Burg schemes employing rectangular, Hamming or "optimum" parabolic windows fail. Data inputs Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar LastBar - bar where to start the prediction PastBars - how many bars back to model LPOrder - order of linear prediction model; 0 to 1 FutBars - how many bars you want to forward predict Things to know Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages. This indicator repaints Further reading A high-resolution modified Burg algorithm for spectral estimation Related Indicators Levinson-Durbin Autocorrelation Extrapolation of Price Weighted Burg AR Spectral Estimate Extrapolation of Price

Garch (1,1) Model The Garch (General Autoregressive Conditional Heteroskedasticity) model is a non-linear time series model that uses past data to forecast future variance. The Garch (1,1) formula is: Garch = (gamma * Long Run Variance) + (alpha * Squared Lagged Returns) + (beta * Lagged Variance) The gamma, alpha, and beta values are all weights used in the Garch calculations. According to RiskMetrics by JP Morgan, the optimal beta weight is 0.94, but this figure is highly disputed in the academic realm. The biggest problem academics and economists have with the 0.94 figure is that JP Morgan used monthly data to come to this number, meaning it does not take other time frames into account. Because of the disputed nature of what beta should be, this script will automatically calculate the beta weight for you in real time, taking into account the time frame you're using and realized variance, by using the Minimum Sum of Squared Errors Method. The gamma and alpha weights are also calculated for you. Even though the Garch formula provides today's projected variance, today's projected deviation is also calculated. This is done by taking the square root of Garch. Additionally, if you want to project the variance or deviation for as many days forward as you want, you can. In order to project the variance and deviation beyond just today, these equations are used: Projected Variance = Long Run Variance + (alpha + beta)^Days Forward * (Garch - Long Run Variance) Projected Deviation = sqrt(Projected Variance) How to use this model: 1st. Decide the type of data you want: Projected Variance in % or Projected Deviation in %. 2nd. Decide how many days you want projected forward. If you input 0, you will get projections for today. If you input 1, you will get projections for tomorrow, and etc. That's it. If you have any further questions, I left detailed comments in the code explaining each step, as best as I could.

Alpha-Sutte Model The Alpha-Sutte model is an ongoing project run by Ansari Saleh Ahmar, a lecturer and researcher at Universitas Negeri Makassar in Indonesia, that attempts to make forecasts for time series like how Arima and Holt-Winters models do. Currently Ahmar and his team have conducted research and published papers comparing the efficacy of the Alpha-Sutte and other models, such as Arima and Holt-Winters, on topics ranging from forecasting Turkey's CPI data, Bitcoin prices, Apple's stock prices, primary energy supply of Indonesia, to infant mortality rates in China. The Alpha-Sutte model in comparison to the other two models listed above shows promise in providing a more accurate forecast, and the project has been able to receive some of its funding from organizations such as the US Agency for International Development, which is a part of the US Federal Government, so maybe the project has some actual merit. How it works: In this model there are four values presented at the top of the window. 1) The first value in blue is the value of the Alpha-Sutte model whose purpose is to forecast the price of the current bar. 2) The second value in yellow is an adaptive version of the Alpha-Sutte model that I made. The purpose of the adaptive Alpha-Sutte model is to expand upon the Alpha-Sutte by allowing new information to be introduced, causing the value to change during the current period, hence the adaptiveness of it. 3) The third value in aqua is the moving average of the low% Sutte line which is a predictive line that is based off of the close and low of the current and previous periods. 4) The fourth value in red is the moving average of the high% Sutte line which is a predictive line that is based off of the close and high of the current and previous periods. Trend signals: If low% Sutte (aqua value/line) is greater than high% Sutte (red value/line) then this is a buy signal. If high% Sutte (red value/line) is greater than low% Sutte (aqua value/line) then this is a sell signal. Caveat: Even though this model's purpose is to forecast the future, will it be able to predict periods of large movements? No, of course not, but it will adjust quickly to try to make more accurate forecasts for the next period. This was also a reason why I made an adaptive version of this model to try to reduce some of the discrepancies between the Alpha Sutte and price when there is a large unexpected move. *WARNING before using this I would highly recommend that you look up "Sutte Indicator" online and read some of the papers about this model before you use this , even though this model has shown merit when compared to Arima and Holt-Winter models this is still an ongoing project.* Hopefully this project will actually come to something in the near future as the calculation for this time series predictive model is much easier to calculate and program in pine editor than something like an Arima model. *Also, if you know how to use R language there is a package for the "Alpha-Sutte model".*