Time series data may be contaminated with different types of outliers. i.e. additive outliers, innovation outliers, level shift and temporary changes. Of course, the effects of these outliers in univariate and multivariate time series are different and detection of outliers in multivariate data are more complicated. Multivariate time series often, modeled using vector autoregressive moving average (VARMA) model and presence of outliers can violate the stationarity assumptions and may lead to wrong modeling, biased estimation and inaccurate prediction. Thus, detection and properly dealing with these data, especially in relation to modeling and parameter estimation of VARMA model is necessary. By detection of outliers, their effects can be removed or robustified and the adjusted data could be prepared for further analysis. The multivariate detection methods, suggested by Baragona and Battaglia (2007) and Cucina, et al. (2014), could not detect the innovational outliers and temporary changes. In this paper, after introducing the VARMA models, the principles of genetic algorithm and its application in detecting outliers are discussed. Then, the Tsay, Pena and Pankratz (TPP) method (Tsay, et al.(2000)) and the genetic algorithm (GA) for detecting different types of outliers in multivariate time series are described. Also, the efficiency of GA and TPP detection methods is discussed using simulation studies and real data. At the end, a conclusion is presented. Material and methods A genetic algorithm makes uses of techniques inspired from evolutionary biology such as selection, mutation, inheritance and recombination to solve a problem. The most commonly employed method in genetic algorithms is to create a group of individuals randomly from a given population. The individuals thus formed are evaluated with the help of the evaluation function provided by the programmer. Individuals are then provided with a score which indirectly highlights the fitness to the given situation. The best two individuals are then used to create one or more offspring, after which random mutations are done on the offspring. Depending on the needs of the application, the procedure continues until an acceptable solution is derived or until a certain number of generations have passed. For minimization of a function, GA operates by first generating, at random or optionally, several minimal solutions to the function, where this set of solutions called the initial population and each solution as a chromosome. Then, using reproductive operators, we combine chromosomes and make a jump into them. If the function of newly produced chromosomes is lower than the previous chromosomes, these chromosomes can be added to the initial population or replaced with chromosomes with less function in this population. This process is repeated until convergence occurs or the end number of iteration obtained. Furthermore, we introduce another method for detecting outliers, i.e. the Tsay Pena and Pankratz (TPP) method. TPP uses some test statistics based on outlier's size and vector autoregressive (VAR) parameters. This method detects outliers in three stages. In stage I, it detects one by one outliers and remove their effects. Iteration continues until no outlier found. In stage II, for detected outlier in stage I, the estimation of outliers effects is obtained simultaneously. Then, outliers with insignificant effects are removed. The VAR parameters re-estimated based on modified series of this stage. In stage III, we repeated stage I and II with new VAR parameters estimation. In each iteration of TPP, an outlier is detected and removed from the series. Then the parameter estimation is obtained from the modified series and the next outlier detection is continued using these estimates. This may lead to biased estimates and wrong detection of the next outlier point. In other words, in the TPP method, one detected outlier hides another outlier (masking), or one detected outlier reveals the usual observation as an outlier (swamping). This method often undetects the type of outliers. But in each iteration of GA, a random pattern of outliers (for testing) is first generated and a temporary modified series is obtained by removing effect of this pattern from series. Then the estimation of the parameters obtained and the detection of this pattern is tested. This method reduces the effect of the previously identified outliers on the full pattern of them. In fact, if the random pattern of all outliers is correctly generated, almost effect of them will be eliminated in the modified series. Therefore, using this temporary modified series, the GA obtains more accurate estimates and detects outliers more accurately. Results and discussion The simulation results confirm the validity of the GA method and the percentage of correct outlier detection in this method is higher than the TPP method. GA, of course, needs more time to calculate. Also, although the VAR model is used in both detection methods, the percentage of correct outlier detection in the VARMA model data is similar to the VAR model. The Gas-furnace data set, called Series J by Box and Jenkins (1994), contains sequentially recorded measurements of two variables (gas rate and CO2) were analyzed and modeled. It was determined that GA and TPP methods detect similar outliers. Fitting the VAR (6) model to these data shows that the variance of input gas error in modified data of GA is reduced by 17% as compared with TPP and the variance of carbon dioxide error in the modified data of GA is reduced by 43% respectively. Conclusion The following conclusions were obtained from this research: In each iteration of the TPP outlier detection method, an outlier is detected and the effect of this point is adjusted. Then the estimation of the parameters is obtained from the modified series and the next point detection continues using these estimates. This may lead to bias of estimates and misdiagnosis of the next point. In other words, using the TPP method, one detected outlier hides another outlier. In the proposed method based on the genetic algorithm in each iteration, first a random design is generated from all outliers and the modified series is obtained from the same design. This reduces the effect of previously detected outliers on revealing the complete design of the outliers. In fact, if the random design of all outliers are generated correctly, the effect of them will be eliminated in the modified series. Thus, with this modified series, GA obtains more accurate estimates and detects outliers more correctly. The simulation results confirm the accuracy of the GA method and the percentage of correct detection of outlier in this method is higher than the TPP approach. Of course, GA requires more time for calculations. [ABSTRACT FROM AUTHOR]