Price and volume occurring at the same point in time both share the same timestamp so in raw form they are equal. By saying volume leads price you're implying a relationship where volume predicts the future direction of price. The validity of this can be measured by using a correlation function and offsetting the index between the independent and dependent values.
You'll have to speak more of correlation function and offsetting the index between values. I don't understand the terms nor what you mean by them. As for price and volume having the same timestamp, an analogy that is similar for me is buying distressed property.
When someone has real property that they want to dispose of, price isn't the primary consideration. It's having a sale NOW. I've had many people walk away from equity, not because it wasn't important to them but that there was something else more important.
For example, I came across a woman who answered a For Sale/For Rent sign, from a property that I just acquired under contract. In the conversation it turned out she was trying to find a place to rent for she was about to sell her home. I asked if she would be interested in selling it today, that I could come over right away. She agreed, and in the following conversation, I discovered her husband sexually molested their teenage daughter in the house. He's in prison from it and since that happened in the house, the state came in and took her other children away. She was surrounded by all this unpleasant memory. The house was in disrepair. The yard was like a dump. She was stuck. She was about to lose it in foreclosure.
All she wanted was having her kids back. The court gave her a plan to do so. Selling the house and moving into a different residence was part of that plan to get her kids back. I was fulfilling her plan by buying her unwanted house on her unwanted kitchen table. A private contract between two willing parties with the same timestamp.
Price did not catalyze the transaction. Her motivation matched with my willingness to be the other side of the transaction did. The Volume of 1 created the sales price. No sales price outside what I was willing to pay did. I've walked away from houses that had lot's of equity but did not pencil out for me. For in real estate, smart money makes money when buying, and gets paid when selling.
The above story describes the power of the moment. Predicting future price is different then anticipating price change. It's a hairbreadth distinction that makes all the difference. For me, in the above example, I didn't have time to know if it was a good deal or not. All I knew is what I was willing to pay, for that was my quantified risk.
So for me, as this applies to markets, volume is an indicator of willingness.
Willingness ebbs and flows just like the tide.
It's willingness that dictates price direction. Volume is an indicator of the willingness to do business.
This perspective that volume leads price, is a perspective that can has tremendous substance and can transform one's observations about the markets as one of being random to one that is orderly. And as many paths go up the mountain, there is the one that has the best views.
Price dictates when to measure volume. The measurement of volume is event based with gates and kills. Not each bar has it's volume measured, knowing which bar does and doesn't is an illuminating experience. Once something is seen, it cannot (without a lot of work) be unseen.
Assuming the existence of consistently applied rules then it's unnecessary for correlation to exist on every bar. It can still be used as a component of a viable strategy. I'm speaking about dry up volume which only occurs occasionally or any other volume condition or requirement that occurs infrequently or is required to occur in conjunction with other events such as price events. Conjunction can be as tight or loose as necessary. Meaning the events don't have to be simultaneous. Variables representing a range of time can be included and thus replace any fixed offset with a fuzzy offset.
I agree DU volume is an important distinction. However, when one adjusts the filters for DU volume, one sees that DU volume occurs more frequently. Lot's of times it's a momentary pause on the DOM. Trends change from two inputs of energy. One is the drying up of the current price volume direction, the other is the entry of new market participants with a different sentiment.
Anyone interested in the topic of "how to measure" if anything leads or lags price might find it worthwhile searching for leading correlation. I am emphasizing the words "how to measure" because previous discussions ignored the simple logic and bliss of offset correlation verses the (mind numbing) standard which is centered correlation (which is where the index of the indep and dep vars are identical). That discussion was interrupted or evolved into an argument about what could and could not be a leading indicator when I emphasized *anything* and everything has the potential to be a leading indicator.
I agree with your last statement and interested in hearing more about the idea of offset correlation.
For instance, it was said (not by me) a moving average logically follows rather than leads price and it can't be any other way. I am in favor of good logic in the right place and at the right time. Like when formulating a simple adjustment to the standard correlation formula. Fortunately I've been blessed with enough (right brain) creativity to keep my logical (left brain) focused on what's important.
I'm in the same logic camp of moving averages. However, even though the logic is sound that MA follows price, the interpretation and resulting action of someone unhindered by that logic is real. The price that this logically unhindered trader is willing to pay is different than the logically supported.
"And/also" provides a better more inclusive perspective than "either/or. "
