Good afternoon. We have studied a one-dimensional time series. There are non-parametric tests that reveal the trend, the type of noise, and so on. Then we need to check for a unit root. Then there is the only statistical method ARIMA, according to which we have studied the time series. Of course, artificial neural networks can also perform predictions. Sincerely, Sharafat Abdurahimovna

Sorry if you have only 11 years of annual or quarterly data your unit root tests will have little power. I presume that you have carried out the unit root tests on the logs of your variables

Good morning explorer. We have a time series derived from the measured network traffic for 5 hours on the backbone. After applying various tests (visual, non-parametric and unit root), it became clear that the series is non-stationary. Further, according to the ARIMA method, actions were taken to obtain forecast data. Tomorrow I fly to the Czech Republic. I wish you success!

Transforming your variables using (-logodds) might help if you are using multivariate regression.

Mohammad Kashour Prince Lassemento Fully

Two popular models that can address nonstationarity are the Autoregressive Integrated Moving Average (ARIMA) model and the Vector Autoregression (VAR) model.

The ARIMA model allows you to incorporate differencing to achieve stationarity. By using differencing, you can transform nonstationary series into stationary series. The ARIMA model can capture short-term dynamics and can be useful for measuring short-term demand elasticities. However, it may not directly capture long-term relationships or equilibrium behavior.

On the other hand, the VAR model is a multivariate extension of the ARIMA model that can capture the interdependencies among multiple variables. It allows you to model the relationships between variables in levels (without differencing) and can capture both short-term and long-term dynamics. The VAR model could be suitable for measuring both short-term and long-term demand elasticities, as it considers the interactions between multiple variables over time.

In terms of limitations, it's important to note that time series modeling, including ARIMA and VAR models, has certain assumptions and limitations. Some limitations to consider include:

1. Causality: Time series models, including VAR models, capture statistical relationships but may not imply causality. Care should be taken when interpreting the estimated elasticities as causal relationships.

2. Model Selection: Selecting the appropriate order or lag length for the ARIMA or VAR model can be challenging. It requires considering statistical criteria, such as AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion), as well as economic and theoretical justifications.

3. Data Requirements: Time series models generally require a sufficient amount of data to estimate the parameters accurately. Having only 11 years of data might limit the robustness of the estimated elasticities.

4. Structural Changes: Time series data can be subject to structural changes, such as shifts in trend or seasonality, which can affect the model's performance. Detecting and accounting for such structural changes is important to ensure accurate modeling.

Good luck!!

Yes, it is possible that some variables are integrated at a higher order than 2, that means they have to be differentiated more than twice to become stationary.

However, the stationarity tests (i.e. unit root tests) are known to be affected by deterministic factors, such as linear or non linear trends and seasonality. Also, structural breaks, either in the trend on in the constant term.

Therefore, make sure you have identified the series correctly in terms of the above (presence of trends and structural breaks) before you proceed with the unit root tests.