There is no specific lower boundary line for autocorrelation, but the accuracy and reliability of your results will improve as you increase your observations.

For autocorrelation analysis, there are no strict rules regarding the minimum length of time series data, but general guidelines suggest the following:

-Minimum Length: A common recommendation is to have at least 50 to 100 observations to obtain a reliable autocorrelation function (ACF). This allows for enough data points to identify patterns.

- More data is better: Longer time series (e.g., 200+ observations) can provide a clearer picture of underlying patterns, trends, and seasonal effects, leading to more robust results.

-Seasonality Consideration: If the data exhibits seasonality, the series should be long enough to capture multiple cycles of the seasonal pattern.

-Stationarity: Ensure that the time series is stationary (constant mean and variance over time) or appropriately differenced, as this is crucial for meaningful autocorrelation analysis.

I do not agree with most answers except those of Muhammad Aliyu Tanko and, of course, Ehsan Ullah. The quality of autocorrelations depends heavily on many causes: mainly the complexity of the process being analyzed (including the existence of a periodical or quasi-periodical component, as said). Their distribution is sensitive to ... autocorrelation, hence the Bartlett formula, itself only valid under strict conditions. Anyway, the limits given by that formula in many packages are generally badly interpreted. Autocorrelations are very sensitive to outliers. In that case, an alternative is provided by rank autocorrelations. For short time series, there exist results for the exact distribution of autocorrelations but under certain conditions. Performing a Monte-Carlo simulation can sometimes be a solution.