Re: 論參數最佳化問題 - 財經

http://www.tradingblox.com/tradingblox/optimization_paradox.htm

節譯

Proper optimization results in a system that is more likely to perform well
in the future, but is less likely to perform as well as the simulation
indicates. So optimization improves the performance of the system while
decreasing the predictive accuracy of the historical results.

適當的最佳化可以提昇系統在未來表現好的可能性，不過不太可能和模擬時跑得一樣好。
也就是說，最佳化可以提昇系統的表現，同時也會降低系統預測的準確性。

I believe that an incomplete understanding of this paradox and its causes has
led many to shy away from optimizing systems out of a fear of over-optimizing
or curve-fitting a system. However, I contend that proper optimization is
always desirable.

對於這個矛盾的現象，和造成它的原因沒有充份的了解的情況下，很多人害怕過度最佳化
，就乾脆不做最佳化了。不過，我的主張是，系統永遠都需要一個適當的最佳化的過程。

NOTE: A complete discussion of the complete process of Proper Optimization is
beyond the scope of this article.

What is a Parameter?

什麼叫做參數？

A well known commercial system is touted by its developer as a better system
because it has only "one parameter". While the developer may have optimized
only one parameter, I believe there are, in fact, many parameters. Many
constant values used in the system, like 2, or 2%, or 5, etc. are actually
parameters that have not been optimized (or perhaps the optimization has been
hidden from the purchasers). By my way of looking at things, this system has
more like five or six actual parameters, even if the developer does not make
it clear, or even believe himself, that these are parameters.

有個程式交易系統，作者招徠顧客說，他的系統比較好，因為它只有一個參數。
雖然作者很可能只有對一個參數做最佳化，不過我相信，
事實上這個系統是有很多參數的。
在這個系統裡使用到的常數，例如 2，2%，或者 5，這些東西事實上都是參數。
他們可能正是沒有被最佳化的參數，或者是最佳化沒有被買程式的人看到而已。
在我看來，這個系統實際上有五六個參數。
要不是作者沒有講清楚，就是他自己也搞不清楚。

Consider a simple moving average crossover system:

拿平均線交叉系統為例：

Using a simple 80 day moving average, buy the next open if the price
closes over the moving average, sell if it closes below the moving average.
The entry stop is 2 ATR below the moving average for longs, 2 ATR above for
shorts. Bet size is 2% of total equity.

使用 80 天的平均線，價格站上平均線就在下一個開盤價時買進，反之則賣出。
停損的話，買進時設在平均線的 2 個 ATR 之下，賣出時設在平均線上。
bet size 設 2%。

How many parameters are there in this system? Many people would answer one
parameter, the number of days in the moving average.I'd answer differently.
First, there is nothing magical about the crossing over the price of the
moving average. Just because we have decided that the exact price of the
moving average is the threshold to buy, this does not mean that one couldn't
choose other prices related to the moving average, say 1/2 ATR higher, or 1
ATR higher, etc.Second, in the stop of 2 ATR, the value 2 is a parameter.
Also with the bet size of 2%, the 2 is a parameter. There is nothing magical
about the 2, one could just as easily use 1%, or 1.5%. So the 2 is just one
value of many that could have been used.Each of these placeholders for values
are parameters.

那麼，這個系統有幾個參數呢？很多人會說一個，就是那 80 天的平均線。
我的回答則不同。首先，價格跨過平均線並沒有什麼神奇的地方。
我們決定跨過平均線就買，並不代表不能選擇另一個跟平均線有關的買進價格，
例如在平均線的 1/2，或 1 ATR 上。再來，停損的 2 ATR 中，2 也是一個參數。
還有，bet size 的 2% 也是一個參數。2 這個數字沒什麼好神奇的，
你當然也可以用 1，或者 1.5%。2 只是眾多可能性之一而已。
所有我們談到的這些，都是參數。

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這個世界多美麗

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