period of time, time period

Period of time and time period are idiomatic expressions.

• The auditor examined the company’s receipts and expenditures over a lengthy period of time.
• This introductory course examines European history by time period.

However, where possible, write concisely by replacing these phrases with period or time.

• The geologist studied the period between the last two ice ages.
• The change of seasons divides the year into four periods (not time periods).
• The Depression was a very difficult time (or period) for many people.