<p>In short, you should apply the test at a point whenever you need to know whether there is a structural break. You may also want to apply it twice once before and after transformation.</p>
<p>For example, common unit root test are biased in the presence of structural break, hence why people came up with alternatives like <a href="https://www.tandfonline.com/doi/abs/10.1198/073500102753410372" rel="nofollow noreferrer">Zivot and Andrews (2002)</a> unit root test or <a href="https://direct.mit.edu/rest/article-abstract/85/4/1082/57440/Minimum-Lagrange-Multiplier-Unit-Root-Test-with" rel="nofollow noreferrer">Lee and Strazicich (2012)</a> unit root test. Hence you would want to test for the structural break before running unit root test in this case.</p>
<p>Afterwards, if you are using estimator that is biased in presence of structural break, you could test again for structural break in the differenced series. Even if there is significant break in levels there might not be significant break in first difference.</p>

CC BY-SA 4.0
2024-07-12T23:31:31.643Z
2024-07-13T08:52:10.843Z
2024-07-13T08:52:10.843Z
1muflon1
<p>I am investigating the price transmission between two inflation indices within the same sector but at different stages of processing. For example, I might be looking at the relationship between raw milk prices and retail cheese prices. My goal is to analyze and estimate the lead-lag relationship and price transmission between these two series using both an Autoregressive Distributed Lag (ADL) model and a Vector Autoregression (VAR) model.</p>
<p>My current workflow involves the following steps:</p>
<ol>
<li>Taking the natural logarithm of both series;</li>
<li>Applying Seasonal-Trend decomposition using LOESS (STL) to remove seasonality;</li>
<li>Differencing the series to achieve stationarity.</li>
</ol>
<p>However, I realize I haven't accounted for potential structural breaks in the data. My question is:</p>
<p><em>At what stage in my workflow should I ideally conduct structural break analysis?</em></p>
<p>Should I:</p>
<ul>
<li>Test for breaks before any transformations (i.e., on the raw data)?</li>
<li>Test after taking the logarithm but before STL decomposition?</li>
<li>Test after STL decomposition but before differencing?</li>
<li>Or should I test for breaks after achieving stationarity (i.e., after differencing)?</li>
</ul>
<p>Given my goal of modeling price transmission using ADL and VAR models, I'd appreciate the community's guidance on when to conduct break testing to ensure the most accurate and reliable estimates of the lead-lag relationship and price transmission dynamics.</p>

<macroeconomics><econometrics><time-series><stochastic-processes>
Structural breaks in price time series: when to test?
André Goulart
# Structural breaks in price time series: when to test?

(Asked by: username_0 on 2024-07-12)

I am investigating the price transmission between two inflation indices within the same sector but at different stages of processing. For example, I might be looking at the relationship between raw milk prices and retail cheese prices. My goal is to analyze and estimate the lead-lag relationship and price transmission between these two series using both an Autoregressive Distributed Lag (ADL) model and a Vector Autoregression (VAR) model.

My current workflow involves the following steps:

1. Taking the natural logarithm of both series;
2. Applying Seasonal-Trend decomposition using LOESS (STL) to remove seasonality;
3. Differencing the series to achieve stationarity.

However, I realize I haven't accounted for potential structural breaks in the data. My question is:

*At what stage in my workflow should I ideally conduct structural break analysis?*

Should I:

* Test for breaks before any transformations (i.e., on the raw data)?
* Test after taking the logarithm but before STL decomposition?
* Test after STL decomposition but before differencing?
* Or should I test for breaks after achieving stationarity (i.e., after differencing)?

Given my goal of modeling price transmission using ADL and VAR models, I'd appreciate the community's guidance on when to conduct break testing to ensure the most accurate and reliable estimates of the lead-lag relationship and price transmission dynamics.

**Tags:** macroeconomics, econometrics, time-series, stochastic-processes


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## 1 answers

### Answer by username_1 on 2024-07-12. Score: 1

In short, you should apply the test at a point whenever you need to know whether there is a structural break. You may also want to apply it twice once before and after transformation.

For example, common unit root test are biased in the presence of structural break, hence why people came up with alternatives like [Zivot and Andrews (2002)](https://www.tandfonline.com/doi/abs/10.1198/073500102753410372) unit root test or [Lee and Strazicich (2012)](https://direct.mit.edu/rest/article-abstract/85/4/1082/57440/Minimum-Lagrange-Multiplier-Unit-Root-Test-with) unit root test. Hence you would want to test for the structural break before running unit root test in this case.

Afterwards, if you are using estimator that is biased in presence of structural break, you could test again for structural break in the differenced series. Even if there is significant break in levels there might not be significant break in first difference.


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