Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 38.81% per annum.
- ABNB price at the close of May 2, 2024 was $158.33 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 88.68% per annum.
- ABNB price at the close of May 2, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of ABNB price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 31, 2022
End date: May 2, 2024
a = 3.9704
b = 0.0009
s = 0.0855
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 38.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0855) – 1
= 40.76%
October 31, 2022 calculations
Top border of price channel:
Exp(Y475)
= Exp(a + b × X475 + 2 × s)
= Exp(a + b × 690 + 2 × s)
= Exp(3.9704 + 0.0009 × 690 + 2 × 0.0855)
= Exp(4.7612)
= $116.89
Bottom border of price channel:
Exp(Y475)
= Exp(a + b × X475 – 2 × s)
= Exp(a + b × 690 – 2 × s)
= Exp(3.9704 + 0.0009 × 690 – 2 × 0.0855)
= Exp(4.4194)
= $83.04
May 2, 2024 calculations
Top border of price channel:
Exp(Y852)
= Exp(a + b × X852 + 2 × s)
= Exp(a + b × 1,239 + 2 × s)
= Exp(3.9704 + 0.0009 × 1,239 + 2 × 0.0855)
= Exp(5.2545)
= $191.42
Bottom border of price channel:
Exp(Y852)
= Exp(a + b × X852 – 2 × s)
= Exp(a + b × 1,239 – 2 × s)
= Exp(3.9704 + 0.0009 × 1,239 – 2 × 0.0855)
= Exp(4.9126)
= $135.99
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 38.81% per annum.
- ABNB price at the close of May 2, 2024 was $158.33 and was inside the primary price channel.
Secondary Trend
Start date: October 13, 2023
End date: May 2, 2024
a = 2.9842
b = 0.0017
s = 0.0415
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 88.68%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0415) – 1
= 18.05%
October 13, 2023 calculations
Top border of price channel:
Exp(Y714)
= Exp(a + b × X714 + 2 × s)
= Exp(a + b × 1,037 + 2 × s)
= Exp(2.9842 + 0.0017 × 1,037 + 2 × 0.0415)
= Exp(4.8709)
= $130.44
Bottom border of price channel:
Exp(Y714)
= Exp(a + b × X714 – 2 × s)
= Exp(a + b × 1,037 – 2 × s)
= Exp(2.9842 + 0.0017 × 1,037 – 2 × 0.0415)
= Exp(4.7050)
= $110.50
May 2, 2024 calculations
Top border of price channel:
Exp(Y852)
= Exp(a + b × X852 + 2 × s)
= Exp(a + b × 1,239 + 2 × s)
= Exp(2.9842 + 0.0017 × 1,239 + 2 × 0.0415)
= Exp(5.2222)
= $185.35
Bottom border of price channel:
Exp(Y852)
= Exp(a + b × X852 – 2 × s)
= Exp(a + b × 1,239 – 2 × s)
= Exp(2.9842 + 0.0017 × 1,239 – 2 × 0.0415)
= Exp(5.0563)
= $157.01
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 88.68% per annum.
- ABNB price at the close of May 2, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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