The main stimulus of the Bank of England review undertaken by Ben Bernanke (2024) was a serious underestimation of UK inflation for 2021-2023. The central bank appears to believe that inflation expectations are pegged at around 2% and assumes that any rise in inflation will be temporary, despite similar significant forecasting errors by other central banks. is. Chairman Bernanke’s 12 recommendations reveal alarming failures, for which Aikman and Barwell (2024) provide extensive commentary.
As the prediction origin advances, successive large prediction errors one step ahead on one side indicate a change in trend. Since the value of the impulse metric is the prediction error at that point in time, the forecast can be “brought back on track” by the impulse metric, which acts as an intercept correction (IC) at the prediction origin (Clements and Hendry 1996). Such forecast errors can be caused by large outliers or measurement errors, step shifts in the process mean, or breaks in the trend. To identify the sources of a series of large same-sign one-step ahead prediction errors and capture sudden rapid changes, a recent paper (Castle et al. 2024) uses a deterministic trend model to Test whether an initial prediction error exists. Two or three large impulse indicators become insignificant when replaced by a broken linear or log-linear trend.
There are three benefits to using impulse metrics to correct errors in the forecast source’s predictions. First, they act as ICs, so the next prediction starts from the prediction origin with unchanged parameter estimates. This leads to larger prediction errors in the case of position shifts and trend shifts, but larger errors in the case of outliers and measurement errors compared to not adding the IC. Second, large prediction errors reveal that the current model needs to be updated, but too few new observations are available to do so in large systems. However, extending a deterministic trend model with a broken trend is easy to implement. Finally, the suitability of linear or log-linear trend expansion can be tested by comprehensive testing of the non-significance of the resulting impulse indicators and of each other (for the underlying theory and Monte Carlo simulations, see the paper Please refer). As new trends and old trends become increasingly divergent, uncorrected results will lead to even larger forecast errors. As a result, even though we have very few observations after the break (only two, and sometimes only one or three), we can estimate the new trend fairly accurately and predict it well until another change occurs. You can continue to do so.
The combination of the COVID-19 pandemic, supply chain disruptions and the energy crisis caused by Russia’s invasion of Ukraine has caused some unexpected and rapid increases in UK inflation. Using a dataset covering 2010(1) to 2024(3), we modeled the log of the monthly Consumer Price Index (in pts) including Office for National Statistics Owner’s Housing Cost (CPIH) shows how quickly they could be detected. ). Track as forecasters make predictions one step ahead as they advance each month from 2021(3) as the first in a multi-step sequence. Initial model (3) until 2021 explains pt by intercept, linear trend, and trend indicator saturation (TIS; see Castle et al. 2019) chosen at 0.01% significance level. Ten shifts between 2010(1) and 2021(3) were selected and the overall trend was corrected to 0.071 (i.e. 0.85% per year). All indicators are zero beyond that date, so the forecast is simply the intercept and overall trend for the 2021 (3) to 2021 (4) forecast (4.45 and 0.071, respectively).
Figure 1(a) shows the fitted value (dotted blue line) and the actual value (pt, solid red line), and the resulting one-step-ahead prediction (vertical line followed by ^), and the interval Shows predictions. Panel (b) shows the next one-step prediction with IC (~, dotted line) and without (^, dashed line), and (c) shows the next one-step prediction with and without (^, dashed line) IC (~, dotted line) and without (~, dashed line). Record a one-step prediction of . Log-linear trend starting in 2021 (3). Estimated from the first two ICs with t-values of 3.2 and 5.4, these are removed. Finally, panel (d) extends the forecast period to 2021(9) and shows that the multistep root mean square forecast error (RMSFE) is 0.15%, so that the broken trend coefficient is reduced from just two observations. Though estimated, it is predicted. The out-of-sample fit is better than the in-sample fit of 0.20%.
Figure 1 Continuous prediction of pt until 2021 (9)
Although we use pt to test and model changes in trends, the annual inflation forecast (indicated by ∆12pt in the chart legend) is predicted by subtracting the log price level 12 months ago. can be derived from. These display the same error bars as the log level, but are centered around annual changes, as shown in Figures 2(a)–(d). It is common after the shift that the first two predictions in (a) and (b) are lower than the previous results.
Figure 2 Continuation forecast of Δ12pt until 2021 (9)
When re-estimating the model up to 2021(9) and then predicting 2021(10), the significant forecast error indicates that a second break has occurred, with the change in 2021(11) from 2021(10) to Confirmed by another large same sign prediction error. Adding the impulse indicators for 2021(9) and 2021(10) and predicting 2021(12) from 2021(11) results in an even larger error, confirming that it is not a step shift.
From Figure 1(d), the break probably started in 2021 (8), so we create a break linear trend starting from that point. This makes the two impulse indicators insignificant, and removing them also removes the large forecast error up to 2022 (3). As shown in Figure 4 below.
However, predicting from 2022(3) to 2022(4) results in another significant failure seen in Figure 3(a). Such a change is not surprising, since by the time this change was observed, Russia’s invasion of Ukraine and the associated energy crisis and rising fuel and food prices had occurred, and from 2022(4) to 2022. This was confirmed by another major error in predicting (5). ) (panel (b)), offset by a broken log-linear trend starting from 2022(3) in panel (c).
Figure 3 Continuous prediction of pt until 2023 (9)
In fact, the model continues to predict fairly accurately up to 17 months into the future, 2023(9), as seen in panel (d). This confirms that medium-term forecasts can be sufficiently accurate despite estimating the latest broken trends from just two pieces of data. Obviously, the condition is that no new breaks occur.
We continue the multistage forecast to 2023(9) to see if this approach is able to capture inflation that initially peaks and then declines. pt’s 17 steps ahead prediction shows that it is indeed possible. Figure 4 plots all the multi-step forecasts for both UK prices and annual inflation. The three broken trends in the pt model estimated to 2022 (4) have positive coefficients, but the annual inflation forecasts from 2022 (5) to 2023 (9) are It captures the first eight drops. This is partly the effect of higher inflation in the previous year than it is now, but it also requires accurate forecasting of pt. Assume that the intermediate one-step-ahead prediction did not produce a significant error, so the forecaster continued to use the same model.
Forecasting from 2023(9) to 2023(10) reveals significant forecast errors and another trend break as pt growth slows. Once again, the broken log-linear trend from 2023(10) produces accurate predictions spanning 2023(11) to 2024(3), but only one non-zero observation is fitted. Figure 4 shows multi-step projections of rising and falling inflation from 2021 (4) to 2024 (3) in pt (panel (a)) and Δ12pt (panel (b)), with vertical spans four breakout episodes. Lines, ellipses highlight interruptions that led to prediction failures. The Bank started raising interest rates from 0.1% in February 2022, and continued to raise them in small increments until 5.25% in August 2023, but the bank has decided to increase interest rates 17 months into 2023 (albeit ex post). Accurate predictions (9) were made in 2022. (4), before most changes were made.
There was a method by Castle et al. (2024) had been available before 2022(4), the same prediction would have been made. One wonders what MPC would have thought of them. Hendry and Muellbauer (2024) estimate that import price inflation, energy shortages and price increases will have a 170% impact on UK inflation in 2022, which is around 3/3 of the peak CPIH rise of 9%. It suggests that it occupies 4. UK inflation rose more slowly in 2023.
Figure 4 All four consecutive forecast sets for pt and Δ12pt up to 2024 (3)
The quarterly forecasts for each December in the Monetary Policy Report (MPR) forecast during the crisis period are shown as symbols in Figure 5, and the earliest equivalent forecasts from our approach are typically marked ∗ or Created by #. Closer to the second MPR projection. Since the dates are shown as vertical lines and the December annual inflation rate is shown as horizontal lines, the forecast error is measured by the deviation of the points from these horizontal lines. Rather than forecasting from a specific date, our approach quickly detects rapid rises to avoid continued forecast failures, as changes cause large one-step forecast errors and break up trends. It only makes sense if you encourage additions.
Figure 5 Monetary Policy Report’s forecast of annual inflation rate
The first such change (denoted as a new coronavirus with a surge in demand after the end of the lockdown) was discovered in 2021 (4) and confirmed by 2021 (5), and the log-linear trend estimation and 2021 It is now possible to predict up to (9) ) when a second shift (supply chain disruption) is detected in 2021 (10). The February 2021 MPR forecast could not have known either shift at that time, and even May could not have known the shift for 2021(10). Once the second shift was discovered, predictions made toward the end of the year were accurate. The next change was in 2022 (3), which was also after the MPR’s initial forecast, but because we detected it by 2022 (5), our approach Compared to the date, it provides a much more accurate year-end forecast (in fact, until 2022). 2023(9)) to avoid unstable overshoots in MPR. Conversely, the change in 2023 (10) occurred in the second half, so forecasting the inflation rate at the end of 2023 is less accurate.
conclusion
An unexpected sudden rise in a trend variable typically creates a series of large, one-step ahead forecast errors of the same sign as the forecast origin advances. When applied to the UK annual inflation rise from 2021 onwards, adding linear or log-linear break trends significantly improves the forecast, showing four rapidly detected trend breaks . These four inherently unpredictable changes are clearly visible in Figure 4, followed by significant forecast errors, and their rapid detection can help reduce the long-term effects of rising and falling inflation. There were only seven large prediction errors across the 36 predictions, rather than systematic prediction failures. Therefore, banks could usefully add this approach to their suite of models to avoid systematic future prediction failures due to unanticipated changes. “Trends are friends until they bend,” and that’s been happening far too often in recent years.
Such an approach quickly detects “tipping points” at the beginning of a rapid increase and its evolution, acting as an early warning system and providing insight into the future, even though we do not know when the next failure will occur. can be provided.
References
Aikman, D and R Barwell (eds.) (2024), Bernanke Review: Answers from the Bank of England Watcher, King’s College London.
Bernanke B (2024), “Forecasting monetary policy making and communication at the Bank of England: A review”, Bank of England Review, April 12.
Castle, JL, JA Doornik, DF Hendry (2024), “Forecasting after the onset of a trend break”, Working Paper, Nuffield College, University of Oxford.
Castle, JL, JA Doornik, DF Hendry, and F Pretis (2019), “Saturation of trend indicators”, Research paper, Nuffield College, University of Oxford.
Clements, MP and DF Hendry (1996), “Intercept Modification and Structural Change,” Journal of Applied Econometrics 11: 475–494.
Hendry, DF and JNJ Muellbauer (2024), “Why did the Bank of England need to review its forecast record?”, Economic Observatory.
