Ez az időszak hosszú.

In standard Hungarian, when ez means this before a noun, it normally appears together with the definite article:

• ez a ... before a consonant
• ez az ... before a vowel

Since időszak starts with a vowel, you get:

• ez az időszak = this period

Compare:

• ez a könyv = this book
• ez az asztal = this table

So ez az is the normal pattern here.

Hungarian usually leaves out the verb to be in the present tense, third person.

So:

• Ez az időszak hosszú. literally looks like This period long.
• But it means This period is long.

This is completely normal in Hungarian.

Compare:

• A ház nagy. = The house is big.
• A könyv érdekes. = The book is interesting.

But in other tenses, or in some other persons, the verb does appear:

• Ez az időszak hosszú volt. = This period was long.
• Ez az időszak hosszú lesz. = This period will be long.
• Én hosszú vagyok would be ungrammatical semantically, but it shows that vagyok can appear in first person.

Because here hosszú is not directly modifying the noun inside the noun phrase; it is the predicate adjective.

So the structure is:

• Ez az időszak = the subject, this period
• hosszú = the predicate, long

That is why it comes after the noun phrase.

Compare the two patterns:

• hosszú időszak = a long period
  
  • adjective directly before the noun
• Ez az időszak hosszú. = This period is long.
  
  • adjective in predicate position

This is very similar to English:

• a long period
• This period is long

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since időszak begins with i, a vowel, the correct form is az:

• az időszak

This is similar to English a/an, but Hungarian uses the distinction only for the definite article, not the indefinite one.

Examples:

• a könyv = the book
• az autó = the car

So:

• ez az időszak not
• ez a időszak

Yes, Hungarian word order is flexible, but changes usually affect focus, emphasis, or style.

The neutral sentence is:

• Ez az időszak hosszú.

You might also hear:

• Hosszú ez az időszak.

That still means This period is long, but it gives more emphasis to long, almost like This period is long or This period really is long.

So the original version is a very natural, neutral way to say it.

Not in the way English speakers may expect from languages with gender or heavy agreement.

Hungarian has:

• no grammatical gender
• much less adjective agreement than many European languages

Here hosszú stays simply hosszú because the subject is singular.

With a plural subject, predicate adjectives often take a plural ending:

• Ezek az időszakok hosszúak. = These periods are long.

But in an attributive phrase, before the noun, the adjective usually does not become plural:

• hosszú időszakok = long periods not
• hosszúak időszakok

So in your sentence, hosszú is exactly the form you should expect.

It is in the nominative form, which is the basic dictionary form of the noun.

In this sentence, időszak is part of the subject:

• Ez az időszak = this period

There is no visible case ending here because the subject is normally in the nominative.

If the noun had another role, you would see a case ending, for example:

• ebben az időszakban = in this period
• ezt az időszakot = this period as a direct object

So időszak here is just the plain base form.

A rough pronunciation guide is:

• Ez ≈ ez
• az ≈ awz or short az
• időszak ≈ ee-doe-saak
• hosszú ≈ hos-soo

A few important points:

• Hungarian stress is usually on the first syllable of each word:
  • EZ az I-dő-szak HOSZ-szú
• ő and ú are long vowels
• sz is pronounced like English s
• s by itself is pronounced like English sh

So in időszak, the sz is an s sound, and in hosszú, the sz is also s.

When ez stands directly before a noun, this ez + article + noun pattern is very common and standard:

• ez a ház = this house
• ez az ember = this person
• ez az időszak = this period

But ez can also stand by itself as a pronoun:

• Ez hosszú. = This is long.
• Ez érdekes. = This is interesting.

So in your sentence, ez is not standing alone; it is part of the noun phrase ez az időszak.