Let's stick with the simple definition of inflation as a decline in the purchasing power of all products over time.
What are the roots of inflation?
This is still an open question as there is always room to debate where and when exactly inflation starts happening due to the imprecise methods to measure it, the velocity which money is exchanged, the human behaviour and etc. Though one thing remains valid and applicable. The supply and demand law. While all economists can't deny that flooding the economy with new created money would generate inflation, there is a huge divergence of the amount which is considered 'flooding'.
At the same time, all economists agree that inflation is an undesired effect as it is a form of taxation.
If the current model is working and one of the main goals of the central banks are control of inflation, how can we have so much inflation now? Jerome Powell, chairman of the FED, answers this one:
This was a just a brief introduction to say that the focus of this work is 100% on the supply side of the currency, which is calculating the amount of XMR circulating in the economy.
Monero supply curve
Let's start with the theoretical supply curve of Monero, which you can see in the graph below. We can simply sum the amount contained in each block mined and see if it is following the emission rules previously agreed by the network consensus. If a miner wants to add a block with a reward value bigger than the expected reward, it will be denied by the network consensus and the block will not be validated. Although it is pretty easy to verify if the new creation of XMR is playing according the rules, it is not sufficient to prove that an unexpected creation of XMR (also named as inflation) happened. Due to the strong privacy preserving schemes in Monero, it is not trivial to evaluate if the transactions are obeying the equation Inputs = Outputs + Fees and an imbalance in this equation could lead to an inflation bug.