The Log Oscillator measures the mean of logarithmic returns, given this data you can assume market expectancy in returns of the mean. When seeing positive Means you can assume positive returns will follow positive returns if positive autocorrelation is present. Vice versa for the other event of negative returns.
How you can effectively use this indicator and oscillator is by looking at a higher time frame and if the oscillator is positive, you can go to a lower timeframe and try to trade in that direction of the market as the expected returns are positive in nature.
You can also spot trend divergences very well as the trend continues but the returns are dropping that means the returns are mean reverting and can have a potential to flip to the other side