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 52.57% per annum.
- MSFT price at the close of May 17, 2024 was $420.21 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.59% per annum.
- MSFT price at the close of May 17, 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 MSFT 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: September 20, 2022
End date: April 17, 2024
a = 3.9925
b = 0.0012
s = 0.0503
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 52.57%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0503) – 1
= 22.30%
September 20, 2022 calculations
Top border of price channel:
Exp(Y841)
= Exp(a + b × X841 + 2 × s)
= Exp(a + b × 1,219 + 2 × s)
= Exp(3.9925 + 0.0012 × 1,219 + 2 × 0.0503)
= Exp(5.5040)
= $245.66
Bottom border of price channel:
Exp(Y841)
= Exp(a + b × X841 – 2 × s)
= Exp(a + b × 1,219 – 2 × s)
= Exp(3.9925 + 0.0012 × 1,219 – 2 × 0.0503)
= Exp(5.3027)
= $200.87
April 17, 2024 calculations
Top border of price channel:
Exp(Y1,236)
= Exp(a + b × X1,236 + 2 × s)
= Exp(a + b × 1,794 + 2 × s)
= Exp(3.9925 + 0.0012 × 1,794 + 2 × 0.0503)
= Exp(6.1694)
= $477.91
Bottom border of price channel:
Exp(Y1,236)
= Exp(a + b × X1,236 – 2 × s)
= Exp(a + b × 1,794 – 2 × s)
= Exp(3.9925 + 0.0012 × 1,794 – 2 × 0.0503)
= Exp(5.9681)
= $390.77
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 52.57% per annum.
- MSFT price at the close of May 17, 2024 was $420.21 and was inside the primary price channel.
Secondary Trend
Start date: January 24, 2024
End date: May 17, 2024
a = 5.8018
b = 0.0001
s = 0.0214
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0214) – 1
= 8.92%
January 24, 2024 calculations
Top border of price channel:
Exp(Y1,178)
= Exp(a + b × X1,178 + 2 × s)
= Exp(a + b × 1,710 + 2 × s)
= Exp(5.8018 + 0.0001 × 1,710 + 2 × 0.0214)
= Exp(6.0549)
= $426.20
Bottom border of price channel:
Exp(Y1,178)
= Exp(a + b × X1,178 – 2 × s)
= Exp(a + b × 1,710 – 2 × s)
= Exp(5.8018 + 0.0001 × 1,710 – 2 × 0.0214)
= Exp(5.9694)
= $391.28
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.8018 + 0.0001 × 1,824 + 2 × 0.0214)
= Exp(6.0689)
= $432.22
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.8018 + 0.0001 × 1,824 – 2 × 0.0214)
= Exp(5.9835)
= $396.81
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.59% per annum.
- MSFT price at the close of May 17, 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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