# Detrended Price Oscillator (DPO): Overview, Calculations

## What Is a Detrended Price Oscillator (DPO)?

A detrended price oscillator, used in technical analysis, strips out price trends in an effort to estimate the length of price cycles from peak to peak or trough to trough.

Unlike other oscillators, such as the stochastic or moving average convergence divergence (MACD), the DPO is not a momentum indicator. It instead highlights peaks and troughs in price, which are used to estimate buy and sell points in line with the historical cycle.

### Key Takeaways

• The detrended price oscillator (DPO) is used for measuring the distance between peaks and troughs in the price/indicator.
• If troughs have historically been about two months apart, that may help a trader make future decisions as they can locate the most recent trough and determine that the next one may occur in about two months.
• Traders can use the estimated future peaks as selling opportunities or the estimated future troughs as buying opportunities.
• The indicator is typically set to look back over 20 to 30 periods.

## The Formula for the Detrended Price Oscillator (DPO) Is:

﻿ \begin{aligned} &DPO=Price~from~\frac{X}{2}+1~periods~ago-X~period~SMA\\ &\textbf{where:}\\ &\text{X = Number of periods used for the look-back period}\\ &\text{SMA = Simple Moving Average}\\ \end{aligned}﻿

### How to Calculate the Detrended Price Oscillator (DPO)

1. Determine a lookback period, such as 20 periods.
2. Find the closing price from x/2 +1 periods ago. If using 20 periods, this is the price from 11 periods ago.
3. Calculate the SMA for the last x periods. In this case, 20.
4. Subtract the SMA value (step 3) from the closing price x/2 +1 periods ago (step 2) to get the DPO value.

## What Does the Detrended Price Oscillator Tell You?

The detrended price oscillator seeks to help a trader identify an asset's price cycle. It does this by comparing an SMA to a historical price that is near the middle of the look-back period.

By looking at historical peaks and troughs on the indicator, which aligned with peaks and troughs in price, traders will typically draw vertical lines at these junctures and then count how much time elapsed between them.

If bottoms are two months apart, that helps assess when the next buying opportunity may come. This is done by isolating the most recent trough in the indicator/price and then projecting the next bottom two months out from there.

If peaks are generally 1.5 months apart, a trader could find the most recent peak and then project that the next peak will occur 1.5 months later. This projected peak/time frame can be used as an opportunity to potentially sell a position before the price retreats.

To further aid with trade timing, the distance between a trough and peak could be used to estimate the length of a long trade, or the distance between a peak and a trough to estimate the length of a short trade.

When the price from x/2+1 periods ago is above the SMA the indicator is positive. When the price from x/2 + 1 periods ago is below the SMA then the indicator is negative.

The detrended price oscillator does not go all the way to the latest price. This is because the DPO is measuring the price x/2 +1 periods relative to the SMA, therefore the indicator will only go up to the x/2 + 1 periods ago. This is OK though because the indicator is meant to highlight historical peaks and troughs.

The indicator ranges, and is also displaced into the past, and therefore isn't a real-time useful gauge for trend direction. By definition, the indicator is not be used for assessing trends. Therefore, determining which trades to take is up to the trader. During an overall uptrend, the cycle bottoms will likely present good buying opportunities, and the peaks good selling opportunities.

## Example of How to Use the Detrended Price Oscillator

In the example below, International Business Machines (IBM) is bottoming approximately every 1.5 to two months. Upon noticing the cycle, look for buy signals that align with this timeframe. Peaks in price are occurring every one to 1.5 months; look for sell/shorting signals that align with this cycle.

## Difference Between the Detrended Price Oscillator (DPO) and Commodity Channel Index (CCI)

Both of these indicators attempt to capture cycles in price moves, although they do it in very different ways. The DPO is primarily used to estimate the time it takes for an asset to move from peak to peak or trough to trough (or peak to trough, or vice versa). The commodity channel index (CCI) is usually bound between +100 and -100, but a breakout from those levels indicates something important is going on, such as a new major trend is beginning. Therefore the CCI is more focused on when a major cycle could be starting or ending, and not the time between the cycles.

## Limitations of Using the Detrended Price Oscillator

The DPO doesn't provide trade signals on its own, but rather is an additional tool to aid in trade timing. It does this by looking at when the price peaked and bottomed in the past. While this information may provide a reference point or baseline for future expectations, there is no guarantee the historical cycle length will repeat in the future. Cycles could get longer or shorter in the future.

The indicator also doesn't factor in the trend. It is up to the trader to determine which direction to trade. If an asset's price is in free fall, it may not be worth buying even at cycle bottoms since the price could keep falling soon anyway.

Not all the peaks and troughs on the DPO will move to the same level. Therefore, it is also important to look at price to mark the important peaks and troughs on the indicator. Sometimes the indicator may not drop much, or move up much, yet the reversal from that level still could be a significant one for the price.