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**KDJ (stochastic oscillator)**

Stochastic oscillator is a momentum indicator which uses support and resistence levels to monitor potential turning points after stock price reaches extremes of recent range.
Stochastic oscillator is composed of three components named K, D, J.

K is calculated as

K=(Close Price - Low_{n})/(High_{n} - Low_{n})

where High_{n} and Low_{n} are the highest and lowest prices in the last n periods (period can be hour, day, week, month, or any other meaningful time frames). K is a value between 0 and 1.

D is calculated as

D=(K_{1} + K_{2} + ... + K_{m})/m

where m represents the number of Ks used to calculate average value. Usually m equals to 3. m is value between 0 and 1

J describes the divergence between K and D. It is calculated as

J=3*K - 2*D

When a crossover happens (i.e K equals to D), J and K and D equal to each other.

In practice, the algorithm above (also called fast stochastic, or stochastic fast) was found too sensitive to the movement of price and often leads to premature turning signal. Stochastic slow was invented to solve this issue and proved to reduce the number of false crossovers. It is calculated by applying a three-period moving average to K of stochastic fast.

K_{slow}=(X_{1} + X_{2} + X_{3})/(Y_{1} + Y_{2} + Y_{3})

where X_{n} represents the nominator of the nth period (of K). Y_{n} represents the denominator of the nth period (of K).

D and J are calculated in the same way as fast stochastic, using K_{slow} instead.

Usually, K below 0.2 or above 0.8 are viewed as signal of oversold or overbought, respectively. When K cross 0.2 in a bearish manner (i.e. from above 0.2 to below 0.2), the stock price will potentially trade at the bottom of the range in a major downtrend. However, when K cross 0.8 in a bullish manner (i.e. from below 0.8 to above 0.8), usually it means the top will soon be reached and a downturn is very close in the future.

In Katelynn's report, weekly stochastic slow is used to monitor mid to mid-long term momentum of a stock. We carefully reviewed hundreds of different stochastic movement patterns and their correlations with price movement, and determined that 9-week periods provide the optimal balance between sensitivity and specificity. Basically, the following algorithms are used to generate the weekly KDJ metrics shown on "Advanced Query" webpage.

%K=((Close Price - Low_{9})/(High_{9} - Low_{9})) * 100

%D=(%K_{1} + %K_{2} + %K_{3})/3

%J=3*%K - 2*%D

For the divergence metric %J, we also provided performance monitor to illustrate the quantile location of %J in corresponding industry, sector, and on the whole market. Since %J has no boundary (i.e. can be less than 0 or greater than 100), it is more effective to judge the level of divergence using quantile loation of %J rather than %J itself.

**Example:** IBM (International Business Machine) has the following weekly KDJ as of 2018-04-27

The data shows K is smaller than D, indicates K line has crossed D line in a bearish manner and is now below D line. Only 14% of industry peers, 10% sector peers, and 11% stocks on the whole market have divergence lower than 5.75, which indicates the oversold level of IBM is above market average during the last 9 weeks. Without considering other covariates, the information above suggests we could put IBM on our radar and watch for turning signal.

Frequently, using weekly KDJ requires investors to watch for stocks with large negative(or positive) divergence, and wait patiently for signal of bullish(or bearish) crossover to take long(or short) position. Making investment decision based on premature signal often leads to significant lose.