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<p>LEARN EXCEL Blog > Econometrics (http Blog page/) My Account (https://spureconomics.com/my- account/) Schedule now! (https://spureconomics.com/schedule-now- econometrics-classes-and-workshops/) Video Tutorials (https://spureconomics.com/courses/) (https://spureconomics.com/#) Manage consent</p><p>ARIMA and SARIMA in Rstudio Viren Rehal Products // Logit and November 14, 2022 // LOGIT AND PROBIT MODEL Probit Model Complete Video Tutorial Series Do it in Rstudio $8.49 $5.49 (https://spureconomics.com/category/econometrics/do-it-in- / Econometrics ARIMA and / Time ARIMA AND SARIMA MODELS Series SARIMA Complete Video Tutorial Series Models // $7.99 $4.99 O Comments (https://spureconomics.com/arima-and- Bundle: 2SLS BUNDLE: 2SLS AND 3SLS and 3SLS Complete Video Tutorial Series $9.99 $6.99 There are several packages available for estimating the ARIMA and SARIMA in Rstudio. Autoregressive Integrated Moving 3SLS Video Average (ARIMA) and Seasonal Autoregressive Integrated Moving 3SLS Tutorial Complete Video Tutorial Series Average (SARIMA) models are often used for forecasting Series purposes. These time series models often provide good $8.49 $5.49 forecasting performance. 2SLS Video 2SLS To understand the estimation procedure of these models, you Tutorial Complete Video Tutorial Series Series can check out the posts on ARIMA Estimation and Model $7.99 $4.99 Selection https://spureconomics.com/arima-estimation-and- model-selection/), and Seasonality and Seasonal-ARIMA models VECM Video (https://spureconomics.com/seasonality-and-seasonal-arima- SPUR CONOMICS VECM Tutorial models/). Complete Video Tutorial Series Series $9.99 $6.99 ARIMA and SARIMA: Video Tutorials Learn Econometrics sarima-models/) Workshops Webinars Personal Classes Group Classes</p><p>Schedule Now! (https://spurecon omics.com/sched SPUR ECONOMICS LEARN AND EXCEL ule-now- econometrics- ARIMA AND classes-and- SARIMA MODELS workshops/) Complete Video Tutorial Series I Blog Categories 4 Tutorials Do it in Rstudio ARIMA Model: Theory AR, MA, ARMA Processes (https://spureconomics.co ACF and PACF Plots m/category/econometrics/d Seasonality: Additive VS Multiplicative SARIMA Model Specification Econometrics Determine the Order of ARIMA/SARIMA Models (https://spureconomics.co Application of ARIMA/SARIMA in R and Stata 4 Graded Quizzes with Explanations Goodness of fit (https://spureconomics.com/course/arima-and-sarima-models/) (https://spureconomics.co m/category/econometrics/g Panel Data Application Of ARIMA And (https://spureconomics.co SARIMA In Rstudio m/category/econometrics/p anel-data/) Simultaneous Equation Models knitr :opts_chunk$set (echo = TRUE) (https://spureconomics.co m/category/econometrics/si library (magrittr) multaneous-equation- models/) library(stargazer) Time Series library(haven) (https://spureconomics.co library (car) me-series/) Microeconomics library(datasets) (https://spureconomics.co library(tseries) m/category/microeconomic library(forecast) tsdata - datasets : AirPassengers Consumer Behaviour view(tsdata) (https://spureconomics.co m/category/microeconomic s/consumer-behaviour/).</p><p>Decompose Demand and Supply (https://spureconomics.co The "decompose" function can be useful in extracting m/category/microeconomic information about the time series. This function attempts to decompose the series into its components: trend, seasonality Costs and the random component. Additionally, we can also choose (https://spureconomics.co the seasonality to be additive or multiplicative. This m/category/microeconomic decomposition can provide valuable insights when choosing the s/theory-of-costs- production-and-producer- order of ARIMA or SARIMA models. equilibrium/costs/) Multi-product firms and plot(tsdata) simultaneous equilibrium (https://spureconomics.co m/category/microeconomic s/theory-of-costs- production-and-producer- equilibrium/multi-product- firms-and-simultaneous- equilibrium/) Production (https://spureconomics.co m/category/microeconomic s/theory-of-costs- production-and-producer- Macroeconomics 1950 1952 1954 1956 1958 1960 (https://spureconomics.co Time m/category/macroeconomi Consumption function dec_add - decompose(tsdata, type = "additive") (https://spureconomics.co dec_mul < - decompose(tsdata, type = "multiplicativ m/category/macroeconomi cs/consumption-function/) plot(dec_add) Investment (https://spureconomics.co m/category/macroeconomi cs/investment/) Development Economics (https://spureconomics.co m/category/development- economics/) Basic Ideas and Theories (https://spureconomics.co m/category/development- economics/basic-ideas- and-theories/)</p><p>Structural Change Decomposition of additive time series (https://spureconomics.co m/category/development- economics/structural- Recent Posts Principal-Agent Problem and Market Failure (https://spureconomics.co 1950 1952 1954 1956 1958 1960 m/principal-agent- Time problem-and-market- Asymmetric Information: plot (dec_mul) Meaning, Types and Market Failure (https://spureconomics.co m/asymmetric- Decomposition of multiplicative time series information-meaning- types-and-market-failure). Market Failure: Definition, Causes and Examples (https://spureconomics.co m/market-failure- definition-causes-and- examples/) Wholesale Price Index (WPI): Meaning and Significance 1950 1952 1954 1956 1958 1960 (https://spureconomics.co Time m/wholesale-price-index- wpi-meaning-and- ACF and PACF plots Consumer Price Index in When choosing the order of p, d and q in the ARIMA models, ACF India (CPI): Role and and PACF can help establish whether the series needs Significance autoregressive terms (p), moving average terms (q). Also, (https://spureconomics.co ACF/PACF can also lend us a hand in deciding the order of m/consumer-price-index- integration (d) of the series. These plots usually give a good in-india-cpi-role-and- starting point in the application of ARIMA models. significance/). Recent Comments acf(tsdata)</p><p>Viren Rehal Series tsdata (https://spureconomics.co m) on Three Core Values of Development (https://spureconomics.co m/three-core-values-of- development/#comment- 2297) Anamulhag (https://Google) on Three Core Values of 0.0 1.0 1.5 Development Lag (https://spureconomics.co m/three-core-values-of- development/#comment- pacf(tsdata) Viren Rehal (https://spureconomics.co Series tsdata m) on Impulse Response Functions after VAR and VECM (https://spureconomics.co m/impulse-response- functions-after-var-and- Dhriti on Impulse Response Functions after VAR and VECM (https://spureconomics.co 0.5 1.0 1.5 m/impulse-response- Lag Viren Rehal acf(diff(tsdata)) (https://spureconomics.co m) on Life-cycle hypothesis: Ando and Modigliani (https://spureconomics.co hypothesis/#comment-</p><p>Series diff(tsdata) 0.0 0.5 1.0 1.5 Lag pacf(diff(tsdata)) Series diff(tsdata) 0.5 1.0 1.5 Lag Estimating ARIMA models There are several packages and functions that can estimate the ARIMA models. Here, we will use the "arima" function to estimate the model. This function allows us to specify a number of arguments for the model. Some of the most useful arguments are: a. order = c(p,d,q): to specifiy the order of ARIMA(p,d,q) where 'P' is the number of autoregressive terms, 'd' is the order of differences and 'q' is the number of moving average terms.</p><p>b. xreg = data: to specify additional independent variables C. seasonal = list(order = c(P,D,Q), period = frequency of season): this argument is used to specify the seasonal component when applying the SARIMA model. Here, 'P' is the number of seasonal autoregressive terms, 'D' is the order of seasonal differences and 'Q' is the number of seasonal moving average terms. d. method = "CSS-ML", "ML" or "CSS": to choose the method used to estimate the ARIMA/SARIMA model where 'ML' refers to Maximum Likelihood estimation, 'CSS' refers to minimzing the Conditional Sum of Squares and is a combination of both in which CSS is used to find starting values and switches to ML after that. arima110 <- arima (tsdata, order = C (1,1,0), xreg init = NULL, method = "ML", optim. method = " err <- resid (arima110) stargazer (arima110, type = "text", title = "ARIMA</p><p>## ## ARIMA (1,1,0) ## ## Dependent variable: ## ## tsdata ## ## ar1 0.307 ## (0.080) ## t = 3.848 ## p = 0.0002 ## ## Observations 143 ## Log Likelihood -698.926 ## sigma2 1,029.292 ## Akaike Inf. Crit. 1,401.853 ## ## Note: *p<0.1; **p<0.05; ***p<0.01 acf(err, lag.max = 36) Series err 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Lag</p><p>pacf(err, lag.max = 36) Series err 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Lag Estimating SARIMA models sarima100 <- arima (tsdata, order = c(1,1,0), seasonal = include.mean = FALSE, method = "ML") stargazer(sarima100, type = "text", title = "SARIMA (1,1,0)(1,0,0,12)" style = "all")</p><p>## ## SARIMA (1,1,0)(1,0,0,12) ## ## Dependent variable: ## ## tsdata ## ## ar1 -0.255*** ## (0.083) ## -3.060 ## p = 0.003 ## sar1 0.959*** ## (0.016) ## = 61.816 ## p = 0.000 ## ## Observations 143 ## Log Likelihood -568.941 ## sigma2 135.245 ## Akaike Inf. Crit. 1,143.883 ## ## Note: *p<0.1; sarima110 - arima(tsdata, order = c(1,1,0), seasonal = include.mean = FALSE, method = "ML") stargazer (sarima110, type = "text", title = "SARIMA (1,1,0) style = "all")</p><p>## ## SARIMA (1,1,0) (1,1,0,12) ## ## Dependent variable: ## ## tsdata ## ## ar1 -0.297*** ## (0.083) ## t = -3.551 ## p = 0.0004 ## sar1 -0.140 ## (0.098) ## t = -1.422 ## p = 0.155 ## ## Observations 131 ## Log Likelihood -507.197 ## sigma2 134.703 ## Akaike Inf. Crit. 1,020.393 ## ## Note: *p<0.1; **p<0.0 ***p<0.01 err_sarima110 - resid(sarima110) acf(err_sarima110, lag.max = 36)</p><p>Series err_sarima110 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Lag pacf(err_sarima110, lag.max = 36) Series err_sarima110 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Lag Another example: SARIMA (1,1,0)(1,1,1,12)</p><p>sarima111 <- - arima (tsdata, order = C (1,1,0), seasonal = (1,1,1 include mean = FALSE, method = "ML") stargazer (sarima111, type = "text", title = "SARIMA (1,1,0)(1,1,1,12)" style = "all")</p><p>## ## SARIMA (1,1,0) (1, 1, 1,12) ## ## Dependent variable: ## ## tsdata ## ## ar1 -0.323*** ## (0.083) ## t = -3.907 ## p = 0.0001 ## sar1 -0.893*** ## (0.276) ## t = -3.234 ## p = 0.002 ## sma1 0.794** ## (0.382) ## t = 2.076 ## p = 0.038 ## ## Observations 131 ## Log Likelihood -506.247 ## sigma2 131.506 ## Akaike Inf. Crit. 1,020.493 ## ## Note: *p<0.1; **p<0.05; ***p<0.01 err_sarima111 < - resid(sarima111) acf(err_sarima111, lag.max = 36)</p><p>Series err_sarima111 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Lag pacf(err_sarima111, lag.max = 36) Series err_sarima111 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Lag Forecasting Usually, the ARIMA and SARIMA models are used for forecasting purposes and they have been observed to perform well. One of the best uses of these models is to predict or forecast into the future.</p><p>forecast_sarima111 - predict (sarima111, n.ahead forecast_s111 forecast (sarima111, h = 36) ts.plot(tsdata, forecast_sarima111$pred) 1950 1955 1960 Time plot (forecast_s111) Forecasts from ARIMA(1,1,0)(1,1,1)[12] 1950 1955 1960 Automatic estimation of ARIMA and SARIMA: auto.arima The "auto.arima" function can be used to estimate ARIMA and SARIMA models. This function automatically chooses the order of the model, performs stationarity tests and chooses the best</p><p>model with the help of Information Criteria (AIC, BIC or AICC). This function performs an iterative procedure to estimate several ARIMA or SARIMA models with different orders of ARIMA(p,d,q) and SARIMA(P,D,Q). Then, it chooses the model With help of AIC, BIC or AICC. The model that minimzes the information criteria is chosen and its results are reported. autoarima - auto. arima (tsdata, trace = TRUE) ## ## [12] : I ## : 1 ## ARIMA(1,1,0)(1,1,0)[12] : ## : 1 ## ARIMA(1,1,0)(0,1,0)[12] ## ARIMA(1,1,0)(0,1,1)[12] ## IMA(1,1,0)(1,1,1) [12] : I ## ARIMA(2,1,0)(0,1,0)[12] : 1 ## ## ARIMA(0,1,1)(0,1,0)[12] : 1 ## ARIMA(2,1,1)(0,1,0)[12] : 1 ## ARIMA(2,1,1)(1,1,0)[12] 1 ## ARIMA(2,1,1)(0,1,1)[12] 1 ## IMA(2,1,1)(1,1,1) [12] : I ## ARIMA(3,1,1)(0,1,0)[12] : 1 ## ARIMA(2,1,2)(0,1,0)[12] : ## ARIMA(1,1,2)(0,1,0)[12] : 1 ## ARIMA(3,1,0)(0,1,0)[12] : 1 ## ARIMA(3,1,2)(0,1,0)[12] : ## ## Best model: ARIMA (2,1,1) (0,1,0) [12] autoarima</p><p>## Series: tsdata ## ARIMA (2,1,1) (0, ## ## Coefficients: ## ar1 ar2 ma1 ## 0.5960 0.2143 -0.9819 ## s.e. 0.0888 0.0880 0.0292 ## ## sigma^2 = 132.3: log likelihood = -504.92 ## AIC=1017.85 AICc=1018.17 BIC=1029.35 plot (forecast (autoarima, h = 36) ) Forecasts from 1950 1955 1960 Further commands in auto.arima The "auto.arima" function provides a larger number of arguments. Some of the important ones are: a. stationary = TRUE: only stationary models are considered b. seasonal = FALSE: only non-seasonal models are considered C. ic = "aic", "bic" or "aicc": information criteria to minimize</p><p>d. trace = TRUE: report all the models that were considered (only order and information criteria are reported) e. allowdrift = TRUE: models with drift are included f. allowmean = TRUE: models with non-zero mean are included g. xreg and method: similar to the previous "arima" command autoarima1 <- - auto.arima(tsdata, trace = TRUE, ic = "aic", method = "ML", test = "kpss", allowdrift = TRUE)</p><p>## ## ARIMA(2,1,2)( (1, 1,1) [12] : 1 ## : 1 ## ARIMA(1,1,0)(1,1,0)[12] 1 ## ARIMA(0,1,1)(0,1,1)[12] 1 ## ARIMA(2,1,2)(0,1,1)[12] : 1 ## ARIMA(2,1,2)(0,1,0)[12] 1 ## ARIMA(2,1,2)(1,1,0)[12] 1 ## ARIMA(1,1,2)(0,1,0)[12] : 1 ## ARIMA(2,1,1)(0,1,0)[12] : 1 ## ARIMA(2,1,1)(1,1,0)[12] ## ARIMA(2,1,1)(0,1,1)[12] : 1 ## ARIMA(2,1,1)(1,1,1)[12] : ## ARIMA(1,1,1)(0,1,0)[12] : 1 ## [12] 1 ## ARIMA(3,1,1)(0,1,0)[12] : 1 ## ARIMA(1,1,0)(0,1,0)[12] : 1 ## ARIMA(3,1,0)(0,1,0)[12] : 1 ## : 1 ## ## Best model: ARIMA (2,1,1) (0, 1,0) [12] autoarima1</p><p>## Series : tsdata ## ARIMA ## ## Coefficients ## ar1 ar2 ma1 ## 0.5960 0.2143 -0.9819 ## s.e. 0.0888 0.0880 0.0292 ## ## sigma^2 = 132.3: log likelihood = -504.92 ## AIC=1017.85 AICc=1018.17 BIC=1029.35 plot (forecast (autoarima1, h = 36) ) Forecasts from ARIMA(2,1,1)(0,1,0)[12] 500 300 100 1950 1955 1960 The "auto.arima" command seems like a great option in every situation. However, it may not always choose the best model. For example, it uses only Information Criteria to choose the model and we might end up choosing a model with autocorrelated residuals. If the purpose is forecasting, it might be better to choose the model with help of forecasting performance instead. Still, it can be an extremely useful function. This website contains affiliate links. When you make a purchase through these links, we may earn a commission at no additional cost to you. 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